They will charge you a small fee to cover the network transaction fee. This fee will be disclosed to you prior to making your withdrawal. You can minimize this fee by waiting until such a time that the bitcoin mempool is empty and transactions are cheaper. Use a site such as https://mempool.space/, and when the mempool has less than 1 vMB of transactions, then that's generally a good time to make a transaction.


Coinbase is fine, and since you are already registered and verified on it, then you have very little reason to consider moving to a new exchange and repeating the whole verification process.

Personally I use decentralized exchanges, which are less newbie friendly but are more secure and more private than a centralized exchange such as Coinbase.