I am new to bitcoin. I have a place that will pay me a small amount of bitcoins, so I need to get a bitcoin address/wallet. Never did this before, but it seems all wallet services want your bank information at some point. Are there any wallets that don't require it?
As in, can I fund them with a Vanilla Visa card (just an example) and then later when I want the money in my hands, can I withdraw to a bitcoin ATM, also without showing ID or giving my bank account info?
Blockchain allows for you to make a wallet w/o showing any ID, however they don't have an exchange.
I highly recommend reading up more on how wallets work before getting too involved with them.
If you want to buy Bitcoin without having to show ID, most of the time smaller exchanges won't require it for a certain amount of money, but then they require it due to regulatory policies of the country they reside in.
Localbitcoins is probably the best exchange for avoiding a lot of ID and being able to fund with cash.