NAKing,
Welcome to the deep end of the pool
I've only been shooting BE pistol (or ANY pistol for that matter) for about 20 months, and I've learned a few things - just a few, mind you...
I strongly suggest you take the majority of your budget and buy a quality .22 pistol. My current pistol is a High Standard Victor, made in Texas. The Texas-made guns are reportedly "iffy" as to quality and are notorious for feeding problems, Mine works fine - I've heard that others have guns that won't shoot at all.
I suggest you start out with a Victor (or other military grip High Standard) made in either Hamden, Conn (first choice) or New Haven (2nd choice). Guns made in either location will outshoot you for the rest of your life, just as they have likely out shot their previous owners for theirs.
I made the "mistake", if you will, of starting off with an inexpensive 22 "just to see if I would stick with it". I bought a Browning Buckmark, and after several iterations of polishing this and tweaking that, I had a gun that I managed to shoot an 832/900 with. Not a bad score for someone shooting a year or so, but at that point, I was likely shooting at the upper limit of the gun. I'm now shooting closer to Master scores, and the fact that I don't is NOT my gun's fault, but mine. I trust my gun to hit point of aim every time, something I couldn't do with the Buckmark as I got better. I do keep the Buckmark in the range box for a loaner to new shooters - it's more than good enough for that.
So take the majority of your budget and get a good .22. Take the rest and get ammo and range time. BTW, I'm shooting Fiocchi, Eley Sport, and Federal 714 standard velocity ammo, none if which costs more than $3 a box and it all works great in my gun. You WILL have to go through several different ammos to find which one(s) your pistol likes, and once you do, buy it by the case so you don't have to worry about running out at the range, and I recommend NOT shooting high velocity ammo - the additional speed doesn't do anything for your accuracy, and can actually cause problems with some pistols.
All the best,
Rob