i don't know what is the best,but so far the better wallets that i ever heard are Electrum and Trezor,
no fees ?
about this 100% about this one,you will never find it because when you try to send your coin,
you need a fee to process it,and without fee ? your transaction will never be processed.
no matter what wallet it will be,none of them will offer you that service or function.
many exchanger recommend you a 'high fee' because they don't want their costumer complaint about their services,
and if you use a 'lower fee' [below average trx fee] more likely you will get it in more than a day,
the higher your trx fees the faster your transaction will be,
check this table about fees and times :
https://bitcoinfees.21.co/Note :
1.Choose the green one if you want your trx will be sent faster
[Prioritize]