I've been a Beretta 92 fan for years, and believe it is great for reliability and combat accuracy. So-so for paper punching. I don't see what all the furor about the safety is. It's a decocker. I don't carry it with the decocker on, and don't know why anybody would, but if I did, it only takes a slight nudge with the knuckle of the shooting hand thumb to have it spring to fire position. It's faster and takes less "reach" for me than reaching for the safety on a 1911 or BHP. The sights are a bit on the small side. Never had a malfunction out of the 4 I've had. Replacing the factory mainspring with a 1911 mainspring will immediately make the trigger better both double and single. The largest and thickest of the 3.
I recently acquired a CZ75BD (decocker) to see what all the fuss was about and I've got to say, they're very nice. Kills me to admit it, but the ergonomics are definitely better than the Beretta's. It's also more accurate (slightly) at punching paper. The barrel is wedged into position at the muzzle end by the slide unlike the Beretta's "floating" muzzle. One thing I really like about it is that you can hold your shooting hand thumb as high as you like without contacting the slide, due to the slide-inside-frame construction. Excellent sight picture. They come with a magazine brake that requires you to pull the magazine out of the well, but it can be fairly easily removed. It really is a fine pistol.
What can you say about the BHP that hasn't been said? It's more ergonomic than the Beretta also, and has that "it's a Browning" look, feel, and image of history. Excellent sight picture also. They all rattle a little after a while (slide to frame) but if it doesn't bother you it's no real problem. Due to its magazine safety, the trigger is usually a bit rough, though it can be taken care of. It's been functionally perfect also.
For paper punching out of the box, I'd have to say CZ-Browning-Beretta in that order.
For combat accuracy, I'd call it a wash.
For reliability, since I've had no trouble with any of them, I'd also call it a wash, though if you look at the Beretta's straight line feed and open top slide, I'd guess it would go longer without a malfunction, unless something broke or I had a bad round. That's just my take, and I may never find out I'm right or wrong. I hope my 3 (Beretta-CZ-Browning) all continue to be perfect.
You hear about the occasional broken locking block and trigger bar and return spring on Berettas, though I've never had the problem. If you visit the CZ site, you hear about broken firing pin retaining roll pins and slide stops. You also hear people raving about CZ USA customer service. I don't remember hearing about any recurring BHP problems, except earlier versions being a little "soft".
Given your target gun criteria, I'd go CZ, as presently they're a couple hundred bucks less than the other 2, and seem to have a great reputation. That's a lot of money for ammo.