What should I set my Gas limit to?

A little new to this so forgive the ignorance! I need to sell some ETH to cover tax expenses from mining, so far I've jsut been keeping ETH in a wallet I use for mining deposits but I've never transferred it anywhere else thus far, to sell or otherwise.

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It looks like Binance is the best option here in the UK fees wise but I'm a little confused by the gas limit that I can set on transfers. On Bitstamp they specify a 70000 gas limit (which seems high) for deposits but Binance doesnt specify?

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Can I leave the gas limit at the default 21000? Can/Should I set it lower if It's not time critical? (it isn't) Do I pay gas fees again once I sell the ETH or is it covered by the exchange fees?