Here is my suggestion. Get a camera that is called the Mobius. It's inexpensive compared to the Go Pro and is a high quality camera, and has a self contained battery, but battery life isn't real long, so an auxiliary battery would be needed.
Here is a link to the RC (radio control website) where these guys have become experts using this camera for their aircraft. In fact, they have worked with the developer to bring this current camera to its great specs.
http://www.rcgroups.com/forums/showthread.php?t=1904559
If you do buy this camera, you will want to reference this website for lots of good info, plus free software to really automate setting for the camera. I have one and I'm impressed with it. The former camera that this group used was commonly referred to as the key chain camera, but for the purpose you stated, the Mobius is the way to go.
The camera uses a micro HDMI card, and can be set to loop when its full, or stop when its full. The camera even works well at night when driving. Check out YouTube for Mobius videos.
Buy only from the sellers that are associated with the manufacture, which are listed on the website I mentioned above.. They are trusted vendor and will sell you the real thing, not a fake.
The camera comes with a slip on mount that has a threaded 1/4 tripod adapter, or anything else that uses a 1/4 mount. There is a suction cup mount that can be purchased separately and its really inexpensive.
For use in the car, what I do, is use a USB cable, and plug the cable into a USB 5V car adapter. These can also be bought cheap off the web, but I think those adapters only work on 12 negative ground. But for your modern car, that will work. Then if you A is 6v, the next easiest way to power the camera for longer periods than the internal battery is to get a USB battery pack. they come in different size capacities, but you won't need a real large one for this application. You will need to recharge the battery pack in the house.
The camera interfaces to your computer via a USB cable.
I bought mine on Ebay from one of the two recommended dealers in China. I just searched ebay for the word Mobius and the first one that came up was one of the recommended dealers, something like Electoponline... and it was for $68 with free shipping. These same dealers also sell the suction cup mount.
Again, be aware of those selling for less, it may not be the same product but a knock off.
Disclaimer: I have not read through the latest posts on the website above, so things may have changed or there may be new models out now.
The group is a RC group and encourages people to first look at existing posts before asking questions, especially the common ones that have been asked over and over again. Read the first set of posts that they list, as those are kept up to date and answer a lot of question you might have and need to know about this camera. Also because they are an RC group and not a Mobius camera group, alternate applications outside of RC stuff are not appreciated by this group. Questions directly related to the camera are fine. So don't ask them about Model A 6V applications, you're likely to not get a friendly response. Just saying (as I'm not a RCers, but found this website really helpful).