...most wigglers wear whatever they feel comfy in and can move freely in in class.. but some will glam up a fair bit more and be hitting the sequins... tho you won't see many in full on cabaret bedlah (bra n belt) - cossies aren't easy to clean so practicality is key! and depending on your teacher (and the dance style) you may well work up a sweat. typically to start out most wear a long flowing gypsyish skirt. take a nice long scarf to tie around your hips - as that is where your attention will be focussed - if you haven't got a coin belt (heaps cheap on ebay). if you don't like dancing barefoot, or get sore feet easily, take ballet pumps. it's helpful also to take a few props - a large old floaty sarong to use as a veil, and maybe a garden cane for stickdance.
you'll find many core moves are similar to those in burly (altho many bellyers will disagree and distance themselves a tad snootily from burly.. it's a bit of an ongoing thing i'm afraid for bellyers who think burly is seedy - but some are embracing it- such as 'bellydance and burlesque' in wolverhampton/rugby)- altho more 'contained' and controlled.. so in many ways it's easier to go from bellying to burly than v.v. i'd say.. expect your bumps to become 'taqs' or hits, your grinds to become hip circles or 'umis', your shimmies to become.. well shimmies or shivers, but often with a different point of focus or technique.
a couple of good links are on the 'mosaic' site and orientaldancer.co.uk.
hope this helps