For $2K, I’d recommend something Wilson Combat(ish) that‘s been well cared for, but used. You may be able to find a Nighthawk with a lot of rounds for around $2K.
I’ve have everything from cheap Colts, to STIs, to my Nighthawk, and my dream gun, a Cabot, sitting in the safe right now, but TBH, the one I’d tell someone to get if they were on a budget is a new Sig 1911. MIM guts, but for about $1K it’s a hell of a shooter.
I bought one for my son a few years ago; found one with a really tight slide to frame fit and spent the first weekend lapping in the slide to the frame. Replaced a lot of the guts with Wilson Combat parts, and added a set of grips:
I’d do one of Nighthawk’s drop-in triggers now though, and may put one in one of my Colts now that I'm thinking about it. Add a really nice barrel, and you’ll be right at your $2K mark, but have a gun you’re not afraid to actually use. And if you do it right, it’ll shoot as well as or better than a gun costing twice as much.
…my best shooting gun, well of the ones that I actually shoot regularly anyway, is still my Nighthawk; almost certainly gonna cost quite a bit more than your $2K budget though:
…and for inspiration: