There's nothing wrong with a 92 for 3 gun. In fact, I started shooting my wife's 92 when I started. With the Mec-Gar AFC magazines and +2 adapters, you'll get 20 rounds in the mag, which is nothing to sneeze at for the majority of courses. Parts are pretty readily available. The stock trigger can be heavy, but most folks put the "D" spring in to reduce the double action pull. The 92 is a heavy gun, which will make it faster to shoot follow up shots - the gun doesn't move much under recoil. My wife's gun has been trouble-free for thousands of rounds.
The negatives you'll hear about using it will include:
Safety: Due to the design of the Beretta safety/decocker, you will start every course of fire with the hammer down. This means your first shot will be double action, every following shot will be single action. Most folks will harp on "transition" like it will take away your birthday. Personally, when the buzzer goes off, I never feel the transition difference. I normally draw to a full target when I can, but I cannot remember a time when the DA pull on the Beretta or the CZ cost me a target. Where the Beretta has a LARGE possibility of biting you is on a stage where you abandon the pistol. When you abandon, the pistol has to be left in a safe condition. For the Beretta, that would mean actuating the safety/decocker before you drop it in the box. That lever is just not always easy to hit on the run with one hand. This is one area where the polymer pistols have an edge - with no external safeties, you drop them in the box and keep running.
Sights: The Beretta sights are OK for a combat pistol, but a 3 dot sighting system is not optimal for a target gun. You can black out the sights with model paint or nail polish, but you're limited. Because the front sight is a part of the slide, you can't easily swap it out for another front sight with a fiber optic. If you like the sights, they're fine, if you don't, you're still stuck with them. There may be places that will mill off the front sight to replace it, but I have to imagine that's going to be an expensive job.
Aftermarket support: While there are a ton of Berettas out there, and parts are available, there is a real lack of competition-specific parts available. You'll be somewhat limited in holsters (Buy a Blade Tech and be done with it). There is not a lot of aftermarket support for items like magazine base pads, trigger groups, etc. This will also mean that gunsmiths are harder to find - it's rare to find a gunsmith that offers trigger jobs on Berettas.
The Beretta 92 is one of my favorite guns. I enjoy shooting them. Along with the CZ, they're the pistols I'm most accurate with and most comfortable shooting. The grip and trigger ergonomics are better for me than the Glocks. The primary issue you're going to run into is the safety/decocker. If you can get past that, I don't see any real reason why you wouldn't shoot that new gun. Throw a "D" spring in there, buy about 3 20 round Mec Gars, get a set of Mil Tac grips (or Hogue wraparounds if your hands are big enough) and shoot the ever loving snot out of it.