"parts available" as in pre-made stuff? Like tranny plates and steering column supports? Those items are very handy I admit, but not needed if you can fabricate. ANY front engine rider is a good one to start with. Some are easier to massage into a racer, but all of them require some level of fabrication. Any of the build threads on here will show how things are done, you simply have to look at what you have and adapt what others have done. My suggestion is to build a prepared chassis and build it the best you can afford. This way you can run in just about any class with the correct size motor and/or drive ratio for that class. USLMRA rules for prepared classes (j/p, a/p, b/p, c/p and s/p and IMOW too) have simular classes in ARMA. So that type of chassis is a great starter platform because it allows you to race just about anywhere at any level.
Now if you have a bunch of mowers to select from, I would pick one that has a peerless 700 series tranny or 600, 820 or 900 transaxles. You will save time and money if you can find riders with those driveline parts already installed. So study up on what the different trans parts look like and go find a mower. Engines can come from any thing. Build that last. Look for other resources too like motorcycle brakes, go-kart parts for steering and frontend. Most important, ask questions, search the build threads, be safe and have fun!