Back on topic:
You'll probably progress much faster if you have both a road bike and a track bike. Neither has to be great, but they should work well. As already mentioned, it's hard to get enough track time unless you have unlimited access. I get a *lot* of track time, and could get more, but I get a lot out of my road miles, including a lot of riding in mountains.
Nothing wrong with clips and straps on the track-- there are still plenty of people who use them and prefer them. I keep some around because they're really reliable, though I use clipless now.