"Bti" will take care of the gnats. mites will need soem sort of spray and other measures... predatory bugs are an option too. products that use pyrethrines kill on contact for mites and probably the gnats too. mites you may need multiple applications.. .the bti bits you top dress every 14-21 days and it'll take about 3 weeks to clear up the gnats if they are bad, now. you can use bti pre-emptively... if your soil/substrate seller stores it outside, i'd acutally recommend always using it. I use it to start every grow, and only if i don't see any hints of gnats i cease using it. it is 99% effective.. you'll still see 1-2 gnats at a time in a room full of 12 pots if the soil came with some
bti will kill the larvea in substrate. sticky traps kill adults... kill multiple stages of life, if possible to speed up process. spiders lay eggs on teh leaves, i believe? as well as elsewhere.. .so, spray under leaves, into each nook and cranny...
there are other kill on contact sprays.. just google the active ingredient and read up on it.. including pyrethrines... and .edu domain is usually a good source.. stay away from anyone selling stuff... they are compromised and not qualified -- http://npic.orst.edu/factsheets/pyrethrins.html -- a good example.
diatamaceous earth (DE) is another options.. insects must physically walk over it to be effective, and it must be dry to be effective. dusting around grow area can help reduce crawling bugs, but won't do much for things that fly. again, if it is wet, it is useless... o not use "pool DE" .. only use foodgrade DE.
with any spray, look for a concetrated bottle that you mix up... it's a 500% or more price difference, often. e.g. look at souther ag concentrated pyrethrin vs any pre-diluted bottle. same with neem and others.
Don't be afriad to use more than one thing, but make sure you aren't using a bunch of things that all cause damage to same parts of plant... 1 alone is no problem but you start spraying 2-3 different things the plant may not tolerate it. diversity of methods attacking different aspects are a good thing if the plant can handle it.