Oh boy, you're gonna get a zillion opinions. And everybody's is the best. Here's my two cents.
If you can, take the PADI or SSI Computer Diving Specialty from your local shop. A good instructor will help you learn about a variety of diving computers, configurations, and capabilities (or at least my course does).
I use a Suunto Vytec, and a Suunto Cobra (one is wrist/transmitter/technical, the other is on a hose) for different diving scenarios. The cool thing is they look and function exactly the same. No problems with either. Although, they are a bit more conservative than the Uwatecs that I mostly see my students with (that is what my shop sells).
Go for a computer that has buttons easy to push, menus easy to read and navigate. Also get one that is Nitrox capable (most are now). Definitely go for air integrated as its not the bottom time that gets you, its that lack of air thing. Having an indication of air time remaining is much more valuable to me. Go for one that includes electronic dive log software. You will love it.
For a dive watch, its the top of the line Citizens Ecodrive for me. Its got a great display and tracks bottom time and depth. It also has an ascent rate alarm. It logs something like 60 dives. I use it as my back up bottom timer and depth guage in technical and cave diving. Never a problem. And never a battery to replace.