In a "boffer" LARP, combat is resolved quickly and easily through the use of foam weaponry. Magic is often handled through spell packets (which are colour coded balls or birdseed filled bags, each of which have specific combat effects), elaborate rituals (which are typically the focus of entire game sessions), or special abilities granted to characters (such as the abilities to temporarily enchant someone with benefits, penalties, or the ability to issue commands to other characters). In a more politically oriented LARP, combat is usually frowned upon, and magic is typically limited to behind-the-scenes effects, where the story focuses on gathering enough people to conduct a ritual effect.
The kinds of stories that work best in each type of LARP can be very different, they typically function most effectively when they work with the strengths of the play style, or when they fill gaps where the fundamental mechanisms of play might otherwise leave things a bit flat. These two types of stories handle things differently, and it often depends on the types of players involved in the game as much as it depends on the chosen rule set.
I've discussed the types of players who tend to be attracted to LARP in previous posts. Most participants don't neatly fall into a single category, they may have tendencies toward one type, they may engage in all the different subcultures that are generally relating to the LARP hobby. The following ideas relating to the ways story might develop with regard to these player types are based on the experiences I've had over the years, generally seeing tendencies rather than fixed patterns of absolutes. It's typically a case of thinking about where these people come from, what their interests a, and why they may have been drawn to the game.
Cosplayers - These players often get into the game because they like to show off their costumes in a more dynamic environment, but they also tend to have a very specific character in mind for their costume. Such a character is often a part of an anime/manga/movie, and has very specific goals that can be easily determined if you know the way the character acts in the particular storyey come from. Don't try to memorise everything about the character this player is portraying, there will probably be a few of these and each of the players will have a very specific interpretation of the character and probably have in-depth knowledge about the character (or their interpretation of it) and there WILL be arguments if you try to get the player to portray something in the character that doesn't go with their interpretation of things (I've seen this dozens of times over the years). Such players may go for combat if that's what their character is about, others will prefer to be social butterflies, not wanting their costumes to be damaged in a melee. If you want such a player to portray a focal character in a story or even just get them a bit more involved in things, do a little bit of research (look up a wiki where the charact might be found), then drop in hints toward the type of story that this character has been involved in, suggest that certain other characters look like allies of that character, or that certain other characters remind them of their enemies in some way. For these players it's all about tying things back to the known properties of the character they are portraying, they are often here to show their devotion to the character they are portraying, and get more people to learn about the character (and the anime/manga/movie) to which they belong. In many cases, these players will latch on to things like that and really get involved after that point.
Actors - These players often get into the game because it allows them to explore character, not necessarily explore a specific character, but explore the inner nature of the role they are portraying. They're not necessarily involved in the game for the combat, but instead to delve into emotions, reveal story through dialogues with other characters or drive story elements of their own through monologues. The way to get players like this more involved in the game is to present them with opportunities to be in the limelight, or opportunities to shine their own light in private conversations that help drive the stories for small groups of others. These players really tend to be social butterflies, its all about the networks and relationships for them, and the opportunity to explore significant choices, then its up to you as a designer/GM to make sure the choices have ramifications in the ongoing story. These are players who will provide the show anship for the game if utilised correctly, they are also the players who will tend to cause the most social problems in the metagame environment if they feel slighted or underappreciated (I've seen both of these effects many times).
Re-enactors - These players may not make the leap to LARP. They often like things to be historically accurate, or specifically accurate to the setting they are re-enacting (eg. Lord of the Rings), they're a bit like cosplayers (but don't tell them that) who like wide sweeping elements of their chosen simulation to match their interpretation of events. Some re-enactors don't make the leap to LARP because they prefer to use metal weapons rather than foam, or because they don't like the idea of magic tainting their battlefield. they like to immerse themselves in environments that match their mental oeuvre...some might put this down to a lack of imagination, some might link this obsessive eye-for-detail to a neuro-atypical condition like Asperger's (though such a condition can be found among many of the other types of playes described here), some might have legitimate issues separating reality from fantasy and they deliberately barricade themselves from certain game elements because they can't handle them. The presence of re-enactors in a game is often predicated on the type of game being played...low fantasy games with little magic that share a strong connection with a specific historical setting might lure a certain type of re-enactors, other games that are specifically designed to emulate a known movie/book/TV property might lure another type of re-enactor. Such players want their stories to reflect the canon events of the setting, if things in the game unfold in the way they understand, then they'll be happy and more than willing to help with other players to get them knowledgeable about the game setting; if things deviate too far from the historical/canon events, they'll be very vocal about it.
Martial Artists - These players are here for the fighting, sometimes practicing twice a week (or more) to maintain a physical edge in combat that the game mechanisms are simply unable to account for. A martial artist player might be portraying a weak peasant who only has a staff (made of foam), but somehow they'll be able to take down other players who are meant to be valiant swordsmen who have been playing the game for months (especially when such veteran players might only get involved in melee once or twice a month during game sessions). A good martial artist player will deliberately play down their combat skills to make someone else look good, the problem is that I've seen too many "bad" martial artist players who prefer to showboat with their combat skills as a player when their character might not be nearly as good. Players such as these come for the fighting, like a Hong Kong Kung Fu movie from the 1970s other story elements are simply events that set up the next fight, or opportunities for them to catch their breath... I've even seen some players from this category resent the story elements that allow other players the opportunity to show off skills where combat isn't the deciding factor. I've been involved in some games where players from this category have been broken of their bad habits (often after they've driven off numerous players who had come to the game for other reasons), and such players can become great drivers for story elements where young adventurer might need training from a master swordsman or veteran soldier, but sometimes it can be necessary to tell players like this to find a more suitable re-enacting or martial group elsewhere if they aren't willing to fit into the larger group.
Tabletop Gamers - These players typically know how to roleplay, they can get into character, they may do crazy accents, they might understand motivations and character agendas. They've typically come to the LARP scene because they want to interact with a larger group of people, because they'd like a more immersive experience, or maybe they want to try something that's a bit different but not too far out of their comfort zone. These players are often more imaginative than many of the others, but this means they rely on their imagination, actions and crazy accents to get into character rather than costuming or appearance (which can prove problematic when they interact with the Cosplayers or Re-enactors who like everything to appear "just right"). Such players are usually very adept with the rule systems and will create characters to maximise their advantages and minimise their weaknesses, Which can be great when trying to work the kinks out of a system, but can be very annoying when other players notice the imbalance. Depending on the GM/DM/MC/"person-running-the-game" that they've had previously, tabletop gamers might be willing to follow their own lead with the creation of story, but those used to a more "railroady" style of play might need explicit instructions and trails of clues to get a story out of the session...such players feel that they need to be told a story rather than engaging in the wider narrative to help tell stories with others. LARP players often need to be independent of the GMs and organisers because there are often a lot of players vying for the attention of those in charge and it can be a while before they get the chance to see everyone. Still, players such as these can be really useful as tools for binsing other player types together to pursue the stories that you might have in place for the session.
Computer Gamers - Even moreso than Tabletop gamers, Computer Gamers often need an explicit series of breadcrumbs to follow. They expect answers at a moments notice, and are used to fiddly game mechanisms being handled in the background while they get on with their adventuring. For better or worse, such players tend to percieve a LARP event as a Live Action MMORPG, perhaps wandering between other players looking for quests to fulfil, but rarely developing ideas of their own because they are used to having the story handed to them on a silver platter. Along with tabletop gamers, these are the players most likely to get upset when martial artist players and re-enactors use their skills trained in the real world rather than the character statistics that they have in the game world (since they are used to the computer handling such things).
Fantasy/Sci-Fi Enthusiasts - Although basically covered in many of the other categories, particularly the re-enactors, players such as these may liken the game to existing settings and stories, be very wary of these types if they start quoting Monty Python, Hitch-Hikers Guide, or similar well known properties as these are capable of bringing a finely crafted game to a standstill.
Consider what types of players are found in a mix, favour the story elements that this player type enjoys. Big battles might be appreciated by a group with a lot of re-enactors in it, one-on-one tournaments might be more appreciated by martial artists, social intrigue (which doesn't damage costumes) might be favoured by cosplayers. Note that I said to favour these types of story elements, vary the mix to ensure other plays in the group have the chance to shine and to make sure the game doesn't stagnate with the same elements repeated over and over.