Nice budget.
350 would get you a great selection of engines. OS Werks Novarossi Alpha RB
Take your pick. Plenty of great engines. Personally I would get a p5...If your new to the racing scene a p5 would give you plenty of power and reliability, later on you can get a vspec RB 10, FMS Nova and so on...
For now a P5 or Werks b5 would be a great race motor for you or even a seasoned expert.