Clearly the lightroom edited image looks much nicer than the less saturated and somewhat drab first shot. As for vignetting, that's a very personal choice and some people love it and others not so much. It's a bit ironic that we buy these expensive lenses that have been designed to reduce and even eliminate vignetting and the first thing people do is add it back with LR/PS.
As for panning, you don't really need much room, you just need the car to go past you from left to right (or right to left). Practicing at a busy street corner will set you up for the next time you're at a race. It's a lot of fun and a nice technique to master, especially if you're planning on doing action shots. You can reproduce something that looks like a panned image in PS but it's not quite the same and certainly not as cool as a true panned image.