Ethermine min payout to wallet is 0.05 every 24h, doesnt cost you anything.
About the custom fee i was talking about my trezor hardware wallet, there are also 3 options of fast normal slow with adequate usd prices on each, but there is also a custom fee option there, the other 3 transfer time ranges from minutes to few hours max, but the custom one i set lowest possible which was under 1 usd which put me in the back of the list, so it took over 8 hours for it to transfer to my exchange app wallet.
I believe you could set ethermine pool payout wallet to binance directly, which would cost you, as mentioned above by adaseb, next to nothing, then in binance you can directly sell eth for your chosen currency, that would cost you based on how much you eth sell, but shouldnt be much, last step is cashing out to your bank, straight to card i think is 1% sends in minutes, but i personally choose sepa transfer which is sent in hours but costs 0.80 euro for me, which is basically also nothing, they sent the money fast its all about how banks in your country work, mine accepts in minutes any transfer.
So there you go, try using binance given deposit wallet address for eth as your payout wallet in ethermine pool website and tell us your experience.
Also i will mention i have no clue about security protocols in this yet, thats why im using a hardware wallet, puts me at ease about my earnings, so i rather pay a bit more, but stay safe that, no matter how small of a chance it is, i wont get hacked.
I realize the payout to the wallet costs nothing, it's the transfer to the exchange that does. Won't they just get that fee somewhere else if I mine directly to Binance? I would like to check it out, but it doesn't seem to have any FAQ that you can get to without me signing up first. I DO NOT want to have to link my bank account, I just want to do something simple and fast like e-transfer where I had my cash in less than an hour. Does it allow that the same way Shakepay does?