Ok, is there a Suzuki dealer nearby?
@doorfx can confirm i believe that is a suzuki vinson 500 engine in your machine, a wet clutch and gasket through suzuki will be substantially cheaper than an arctic cat dealer if that is the case. Personally I would get a gasket for that case side, your belt housing gasket should be fine and re-usable, but the next gasket in will come off in pieces.
in my opinion-
1 wet clutch,
1 wet clutch housing gasket
Oil Filter
get 1-2 oil changes of the cheapest wet clutch safe 10-40 dinosaur oil you can get (some guys use Rotella i believe for the JASO MA certified oil)
get a jug of the good 10-40 oil you want to run.
You will need to inspect the "wet clutch housing" or i like to call it a drum because that's what the wet clutch grips inside of and turns like a drum brake, housing is such an odd term. hopefully it survived the fallout, light grooving should be ok, but if there is any major wear or damage or burns then you may need a new one.
In my opinion, if it was me, I would dump the oil that is in there now out, refill the engine with cheap wet clutch safe oil start the engine build oil pressure, circulate the oil, dump it,
If you are paranoid repeat this again.
Once you have flushed the oil out 1 or 2x I would drain the oil and split the case open to start looking at problems. don't forget to swap your oil filter.
when your new wet clutch comes in they are supposed to be oil soaked for a certain amount of time (i think its a few hours, i was away so i soaked it for a few weeks) if you start soaking new wet clutch the day before you plan to assemble it, you should be ok.
if you clean everything out really good while in there the 1 way bearing is oil bathed and is not concerned about what oil it is bathed in, just lubricant. it's the friction modifier in automotive oils that toasts the wet clutch.