With the problems with Bluetooth still existing, what I'd do (and I did) is to go into a store that sells head units (what I was looking for was available at Walmart, so that's where I went) and find head units that fit your needs. Then try co pair and connect your phone to each one. Eliminate the ones it won't connect to. Then see what prices you can find for the ones you can use online.
Is it a good idea? I never leave town, so I don't need anything but the radio for listening to the radio, but if you're going to be on the road, listening to some streaming station online would be a better idea, so no radio would be a good idea. No GPS? You have GPS in your phone, and if it connects via Bluetooth, you'll get your turn-by-turn out of the speakers.
Steering wheel controls? That's usually proprietary, so if you have them on your steering wheel you probably won't be able to use those, you'll have to use the ones that come with the head unit (and run a cable from the dash to the wheel, or pay someone to install it for you. And if you're going that route, go into a store with a good reputation and work the whole thing out with them - they'd be in a better position to help you than we would. They could probably even wire the existing controls to a new head unit.)
Android Auto? If you're going to be taking calls and sending and receiving texts (not a good idea - ask any highway patrolman), that might be a good idea - but there are other apps that do the same things. Just make sure that Google can communicate with them.