Is 12 by 20 feet garage big enough for today's cars?
I have a few comments:


That is a pretty enormous car but looking online it seems like you should have about 2.5 feet on either side. That seems like enough. I assume you'll get more comfortable about maneuvering in the garage once you've done it a few times.
If you are concerned about the length, the are a variety of tools that can help you pull in far enough to close the door but no further. My favorite low-tech way is a tennis ball hanging from the ceiling by a string that has been adjusted so that it touches the windshield when you have pulled in just far enough. There are also high-tech gadgets that use radar and lasers.
If you want to park your car in the garage at all you I think should keep the space clear. If you slowly add various tools, boxes, extra stuff you will have a hard time when the forecast calls for snow and you need to spend 3 hours finding somewhere to put all that stuff. In my opinion it's just easier to have it be a car space or not.