[T. O'Heir]

"...a decent bowling pin gun..." A stock 'Milspec' Springfield with a trigger job and chamfering the chamber would be a decent pin gun. High visibilty factory sights.
"...you're gonna need more than $1200..." Nope. Good sights and a trigger job is enough. Good ammo is critical though.
"...if jacketed bullets were used a lot..." Too expensive to shoot reguarly. Cast 230 grain RN's or FP's with 4.5 grains of Bullseye works well out of my Series 70 Colt. Scary accurate.
"...become good enough to do a few competitions..." Go shoot the competitions anyway and don't worry about placing. It's great fun and you'll meet some of the best people you'll ever meet. Most of whom will bend over backwards to help you.
Whichever pistol you buy(find a used Series 70 Colt) will need a trigger job. High visiblity(big, front and rear), adjustable, sights are best. And you have to sight in with the ammo you intend using. If you aren't reloading now, you will be. Factory ammo is expensive no matter what bullet it's loaded with.. As are jacketed bullets, previously mentioned, for reloading. If you're not reloading now, you will be.