$36 is about 0.008
BTC and most exchanges have minimum trade volume of 0.0001
BTC so you don't have any issues there.
the trading fees are also nearly the same in most exchanges. they are near 0.2% of each trade. for example on 0.008
BTC you will pay 0.000016
BTC or 1600 satoshi.
the only thing left is verification.
if you want to trade bitcoin with fiat, they will ask you some sort of verification without exception because that is what fiat world requires. there may be an exception somewhere that lets you deposit bitcoin trade with fiat and in the end withdraw bitcoin not fiat without verification.
but when you trade altcoins with bitcoin, most of them don't ask for verification.
bittrex is the next best thing but they will restrict your withdrawing amount if you are not verified. I think it is restricted to 0.025
BTC per day but I may be wrong.
other small exchanges like crptopia have small volume but they are good enough and don't ask for verification.
I am homeless.
I am very curious to know how you are planning on making the trades then!