Personally, I like Tsuki's idea of the missions in the different regions.
Perhaps students can earn these special missions? With a point system, they can buy a license to leave campus and go on a mission somewhere in the world?
School excursions to different regions, with the ability to catch more pokémon from that region while they're there
This way, they'll have a chance to catch anything from that region while on the excursion, while others may want to stay at the school and enjoy the surges. These excursions can be for single classes, as well as for the entire school
What about a way to combine the two? Maybe set up a system so that once they earn a certain ammount of points by winning battles in battle class, getting good answers participating in school events turning in assignments, ect. Once they reach that amount of points they can leave to earn one badge from a region, maybe even 2 by 2s, then come back to the school and work towards the next one.
House points ( at the risk of sounding like a Harry Potter fanatic and more of a dork than I am XD ) could also be a way. Like all the points from flame, splash, or leaf are added as a competition and the winner house gets a field trip to a new place they haven't been to and some uber prize ( maybe a way to evolve their pokemon since the evolutionary items at the store are quite the pretty penny or a chance to submit 3-6 pokemon to the pokesurge grow a level for one pokemon of their party without the four-posts-per-level rule...yeah my prize ideas not as good as my earn-the-prize-idea I'm afraid lol )
For Team Darkrai members it could go by how many successful missions they achieve. Seeing as they're against the school mainly and the society within it grunts would probably start by making scouting missions around the school and maybe sinnoh which will limit the pokemon they can catch to the ones in sinnoh and the pokesurge.
This will hopefully encourage posting since it's four post ( no one liners) for a battle and thanks to level up system you need a certain ammount of battle post to get to the next level. And not only when it comes to catching pokemon but also in events and classes. And do their homework! ( and I had the oddest need to add 'and eat their veggies! lol ) It will also leave it up to each person whether they are more comfortable posting more by the game or rp-ing for their character ( in the school setting)
And then there's the events themselves this is a school, and i at least rather like that theme. It makes it different from other guilds and gives a learning curve to people who may not know the ropes of pokemon rp-ing ( as someone who watched the anime and never played a game until emerald, the whole stat-numbers things get pretty confusing. I've actually had trouble rp-ing for pokemon before until I found this guild. ) or likes character development and rp-ing over battle math.
I didn't have much of a social life in High School but right off the top of my head, there's dances ( I remember there being way too many dances for my liking, homecoming, spring fling, formals, winter balls, halloween dances, Graduation dance...or prom I guess they call it here, competitions ( like you have for school sports but for contests and battle ) maybe even a breeding competition...that one I'm not sure how it would work, maybe submit one pokemon they bred and be judge by their moves,their parents...originality, maybe purpose..idk.
Clubs, maybe have an art club ( anyone from both he the art class and not the art class) help decorate for events, have the students themselves contribute something to the events but have a slot system so it gets people post more ( maybe go with the whole points system) Battle club ( against not specific to battle mayor) can be the ones who really know what they're doing battle wise and like Tsuki said focus more on missions and adventure as they won't need as much class time. Contest club can have trips to contests in the region. Investigatons can maybe visit almia regions or officer Jenny's throughout the regions. Teachers themselves ( meaning the crew) could come up for small events for their classes. Not every day..just something special like in regular schools.
Festivals for fall winter spring. Maybe get the regions so we can post for the students during summer vacation ( if some rp-ers want their oc's to be friends or whatever )
As far as events go maybe do fossil digs ( which were mentioned in the rules ) have a dice system for which fossil pokemon you dig up and only be able to catch a certain amount to keep it all even and fair. Sign up sheets to make it more like a school event and get people to pay attention to the guild.
Swarms of pokemon like there are sometimes in the gen 3 games, maybe rare ones you only find in swarms.
Pokemon to be caught during winter break ( either by type or by winter colors) and other seasons. Maybe even summer since it's a boarding school so students can stay through the summer, summer events.
Having a clock/date thing might be a good idea, not only because some pokemon can be found during morning an night or evolve during morning and night but when you rp for your ocs it'd be nice to know whether to put 'he'd been training all night' or 'he went to the cafeteria for breakfast'. Maybe set it after the halloween event so everyone can be in the same time-fram. It doesn't have to be by the hour. 'Morning' can last for a day or two for every one to get their posts done either at the dorms, cafe, or catching the pokemon that only show around morning. Then afternoon then Night.
It might also help if the minor classes all have their own slots. Since as Tsuki mentioned it's hard for everyone to get together. The teachers ( again meaning crew) could meet up and each choose a time that is best for them to post their class depending on where they live how busy they are and other factors, they can even request switching class order with another teacher if something comes up. The classes would be shorter but everyone would get to go and hopefully there would be less confusion. I love the flexibility in this guild and hope that doesn't change but maybe that bit of structure might help. An announcement could be the 'bell' that announces when a class ends and another begins, maybe giving some time to catch a pokemon in between ( though not so much that it lags)
That's all I can think of off the top of my head. Hope it helps.
One concern I have is is the guild gonna changed a lot? Is it gonna take the numbers system you use on the ones that go by the game? Cause that's a bit hard to keep up with.