What kind of competition for what kind of project?
Certainly kraig's police surplus .38 Special would get you into IDPA SSR, USPSA Revolver, and ICORE, also PPC if you are a LEO, at a moderate cost. You could even try NRA Conventional (bullseye) shooting with one.
If you want an auto and don't mind paying more for one, the leading guns in the IDPA SSP where I shoot, as well as USPSA Production, are Glocks, Smith & Wesson M&P, and Springfield XD. They all have striker fired actions, no manual safety, and consistent (not great, but consistent for all shots) trigger pulls. Double action autos like Sig Sauer and Beretta are less common but still seen.
If your project covers conventional (bullseye) or metallic silhouette, the best way to start is with a good .22 like a Browning Buckmark or Ruger Mk III.