I really have to question how Binance is pulling off basically no fee trading. There's something not right as if they may be hit with pretty hard regulation. Add in the Brian Brooks lasting two months as CEO of .US and Catherine Coley's short stint (and disappearance). I would transfer some of my funds over since they seemed to cleanup the customer service nightmare but it seems like too much unknown risk.
You can buy daily BTC/ETH which is delivered at 4pm, and the fee is a flat $5 per coin (so ~0.01% at the current BTC price). BTC is traded in 0.01 increments and ETH in 0.1 increments.
Caveat is that only wire deposits are accepted, so the wire fees plus network fees (if you withdraw your coins) can raise this cost substantially if you only trade small amounts.