There will be to sides to the Race Track, you can either enter your own Houndour or Houndoom (it's a two tier thing), or you can bet on the prexisting ones.
If you enter your own, you will be able to win prizes which may vary between a few things. However if you place a bet you will only win money back.
Now I also mentioned Houndoom above, think of it as a child and adult race. The Houndour race is just the standard race however the Houndoom races are slightly harder and require your Houndoom's to be high level and very fast - so yes, your stats will effect the outcome.