You're probably talking about online wallets, this is why I see you confused. If you used a non-custodian wallet (like electrum) you would notice that every one of them offers you such feature. You set the fee, by yourself, not via some centralized services. Download it, install it and experience with it.

As ranochigo said, consider using Bech32 addresses (those that start with bc1, AKA Segwit), because they're reducing your fees by a lot.

PS: Stop using online wallets!

What do you mean by "typical"? The fees that are chosen usually from the majority? The median fee?

Online wallets are generally not great if you're looking to minimize transaction fees, some of them don't implement segwit and some of the have poor fees estimation as well. Custodial wallets often charges their users more fees than necessary when sending Bitcoins. That is not the only reason why you shouldn't use them.

Transaction fees are not dependent on the wallet that you're using though it can be. Wherever possible, use Segwit (bc1) addresses to have the lowest fees or nested segwit if you want backwards compatibility. Electrum and Bitcoin Core both have decent fees estimation and features but you can also refer to mempool.space as a reference to adjust your fees as well.