I'm a fan of starting with the Mira, so I've used that for the Lightweight K, Sunday Cup, Clubman Cup, and FF Challenge before I buy my next car. However, in my recent quest for 100% wins & 100% gold, I began with the B-license Miata. That makes things a little simpler. I used it in the Sunday Cup, Clubman Cup, FR Challenge, NA Challenge, and Spider & Roadster races before going to another car and kept the mods very cheap overall after the 18K initial investment.
So use your first car, staying away from mods over 10K (tires are the only exception here) and trying to keep everything as cheap as possible, for as many races as you can. Then, buy yourself a nice second car (I highly recommend either the Honda Integra Type R or the Mitsubishi Lancer Evolution VI RS) and go to town.