First thing you need to decide is what kind of Bullseye matches you are going to fire. The first type is Service Pistol. You can have very limited external modifications to the pistol, but you can have a match barrel, match mechanical sights, and a crisp, match trigger set to 4 lbs. It shoots the 230 grain standard or match Ball ammunition (Hardball). The second type is the NRA match .45. It can have a 3.5 lb trigger, adjustable or electronic (red dot) sights, extended front sights, target grips with palm shelf, and is set up for light target loads such as 185 grain bullet w/3.5 grains of Bullseye (softball or Wadcutter). A useful reference for the allowable modifications is the NRA Pistol Rulebook.
Now how do you get there? One, you could buy a match Service Pistol or a NRA Match pistol from Baer, Kimber, or others, and expect to pay 1200-1500 bucks. Another way is to get a Springfield basic 1911 and build it up to match pistol standards over time, as your finances allow. The three basic requirements are a match barrel (Kart and Bar-Sto make good ones), Match sights (Bomar for mechanical, UltraDot for red dot), and a match trigger (Videcki is cost effective). You don't need these all at once. Match trigger first, then sights, finally the match barrel. If you want to do the fitting yourself, get a copy of the Kuhnhausen .45 Shop Manual, and the Hallock's .45 Auto Handbook to see what you are in for.
Another alternative to building and buying one outright is to find some Bullseye shooters. Almost everyone will have a match .45 for sale as they move up to better (more expensive) equipment, in their never ending quest for just a few more points.
