Do what I did. Go to a range that charges a 1 time rental for guns, where you can switch up as much as you want.
Buy a box of 9mm, a box of 40 S&W, and a box of .45 ACP
Why do I say these? Cause they are semi-auto rounds. I prefer them to revolvers. Your preference may be different.
Then, pick up a glock 9mm, a sig 9mm, and a Ruger SR9. I say SR9 cause I haven't shot it yet, but I hear good things.
Grab a Ruger p944, glock 22/23, and a S&W .40 caliber(don't remember the name)
Test them all out
Then grab a sig .45, a ruger 45, either the p90/p345, and a glock .45 but the glock 45's need different ammo, so try to run something different, maybe a 1911 model.
Now, why do I say ruger for all 3? According to your budget, they would fit very well. Then do what I did again. Shoot them, make NOTES on the ones you liked, and what you did/did not like about them. Your answers will surprise you!
Next, pick one you like the best, and research it to DEATH! I mean death. I ended up picking up a P345 myself after firing it enough, checking with my dad, and reviewing any problems/incidents with it. Turns out, the only problem would be dry firing without the mag in place, which doesn't bother me, cause I got snap caps. About 3 months of looking and reading before I picked it up.
I suggest you seriously do the same so you don't have a buyer's regret when the gun does or doesn't do something you haven't factored in.