I see very few HiPowers at IDPA/USPSA matches, for example. Likely due to the mag disconnect.
The mag disconnect can be easily removed. The reason for it being so rare in USPSA is that it's not really competitive in any division. Its best fit is in Limited-10 and even then you're typically not running a mag-well and you're shooting minor. It just doesn't fit any one too good.
Anyways, on to my recommendations:
You really need to figure out what types of pistol games you want to play, because that will determine which pistol would be optimal. I personally shoot USPSA normally. I've shot IDPA and Steel Challenge in fun matches (never an official match) and based on that experience I can tolerate Steel Challenge, but I know IDPA isn't for me.
Each person has their preferences though, so you should visit matches of all types (even ICORE if you can find a local club), and see what you like.
Now, on to my USPSA recommendations (Steel Challenge has matching divisions for these so it applies here too):
USPSA has several divisions: Production, Single-stack, Revolver, Limited, Limited-10, and Open.
Production is sometimes called a beginner division, but that's a bit of a misnomer. I'd consider it more of a "budget" division. Your targeted $700 budget can get you setup in production with a pistol that you could win nationals with if you had the personal skills to match. It's mostly stock pistols with some basic modifications allowed (basically internal-only modifications and sight changes). No more than 10-rounds in a magazine. All guns are always scored minor which makes 9mm the most competitive round here (also good for the wallet). Only striker-fired guns or double-actions are allowed here - no single action. The striker-fired guns by far dominate this division due to the consistent trigger pull. Glocks are most common, with M&P's in a somewhat distant 2nd. XD's have been increasing slowly in popularity too. Hammer-fired double action guns are legal, but not really popular here.
FWIW, I shoot a S&W M&P 9L in production.
Single-stack: This is kinda like a special production division specifically set aside for 1911's. Mag capacity is capped at 8 if you're shooting major PF, or 10 if shooting minor.
Revolvers: Self explanitory.
Limited: As odd as it sounds, there's not many limitations here.
As long as your gun fits in a given box, has a magazine of restricted length, don't use a compensator and doesn't use any optical sighting (red dots), then it fits limited. This is dominated by really expensive double-stack 1911's in .40S&W. Your $700 can get you a gun to shoot in this division, but it won't be truly competitive.
Limited-10: Same as limited but no more than 10 rounds in a mag.
Open: Except for fitting in a rather generous box and a magazine length limit - pretty much anything goes here. Insanely fast shooting "race guns". Everything - even a "poor man's" open gun built in a converted Glock - is going to run into the thousands.
My advice: it sounds like you're young, probably on a limited budget. Get a Glock 34. It's got a nice long barrel, plenty of aftermarket accessories, and is basically the quintessential USPSA Production gun. With a good .22LR upper, you can also shoot rimfire in Steel Challenge if you wish. Overall I think it'll give you the most bang for your buck.
The M&P is also available and a good gun - like I said its what I shoot. It's subjective, but if find it to have a better grip than the Glock. My only complaint is that the max barrel length on an M&P is 5" compared to 5.3" on the Glock 34. There's also no .22 conversion currently out for it.