again it all depends on what costume you want. but here's a list of things i think work for various types of costumes.
cotton. it can be very light so with as many layers as you might need, you won't get too hot, depending on the color. for a darker color such as black or navy, if you're going to layer it, you'll want a lighter weight (aka a thinner cotton). as always, pick a heavier weight if it's going to be a light color such as white so it won't be so see-through. it's a good choice because it comes in various colors and patterns.
twill. it's a heavy duty fabric. think of how tough denim is. well it's sort of similar but retains a more formal appearance. it also comes in a variety of colors so you can find the perfect shade for any hetalia cosplay, fma uniforms, etc. because of it's thickness, it's not too unrealistic a choice if whatever your costume is were a real uniform.
depending on the look, cotton is a good bet. cotton is, in my opinion, best because in a lolita-inspired outfit, it's usually taken the look on a poofy skirt. to achieve this, you'll need to fit a petticoat under it. cotton will not weigh down the petticoat yet still look nice.
female school uniforms/sailor-fuku:
cotton or linen. i use cotton. i know for a fact that cotton pleats very well, which is usually seen in these types of uniforms. i haven't used linen yet but i hear it holds just as well. it's also a nice texture and comes in enough colors to compensate for all the weird uniforms out there. and if you can't find the right color, cotton is easily dye-able because it's a natural fiber.
gakuran or suits:
is a gakuran. for this i would suggest a suiting material, or if it's a really weird color maybe twill. suiting material is for suits. kinda speaks for itself.
there are a few materials to choose from. cotton lycra
(think that stretchy t-shirt material), spandex
, stretch vinyl
. any sort of stretchy material. cotton lycra is more matte, spandex is more common in pre-made bodysuits (which you'll want to look into if you're a relatively new sewer). cotton lycra i think looks amazing, but i understand why people don't always use it. not to scare anyone away, but it breathes horribly and you will probably sweat a lot in it.
leather substitute/boot covers, orgXIII coats:
vinyl, no doubt about it. it looks like leather, feels like leather, but doesn't cost as much as leather.
tulle or netting. it's stiff and will hold it's poof very well. i believe organdy is also used but don't quote me on that haha.
here are some fabrics i recommend staying away from.
satin: i mean the cheap-o kind. it'll show all your sewing flaws and is too shiny for any sort of forgiveness. it also even looks cheap.
broadcloth: it's pretty much cotton. but it's TOOOOO thin. like...you can see through it. really.
those are really the two most hated fabrics in cosplay.