For theater you usually want something with a
manual mode that you can custom set the aperture,
shutter speed, and
ISO levels in. You also want a decent optical
zoom. Digital
zoom is worthless.
With a DSLR
system, you have a digital camera body with interchangeable lenses. It's great because you can always use the best
lens for whatever you're shooting that day. You can use a short
zoom lens if you're taking photos from the 3rd row, or you can
whip out your long
throw lens if you're shooting from the back of the theater. But don't plan on getting one of these in the $150-$250 range. I've been building up my DSLR
system over several years and I probably have $7000 invested into it and special insurance to
cover loss, theft, and accidental damage.
The big key is, get something you can tweak the
manual settings on. Point-and-shoot cameras generally suck for photographing theater because they have a hard time adjusting to the varying lighting intensities across scenes and continuously try to re-auto-focus, meaning you miss critical opportunities for shots while your camera is fighting with itself to get in focus. If you get something with a good
zoom lens and learn how to tweak the camera settings, you can usually pull off some decent shots for not a huge amount of money. Also don't forget to
pick up a tripod. For some scenes you will want to photograph extremely low-lit looks, and to do so you'll need to lower your
shutter speed. If you do this on a tripod, you'll get a crisp,
clear photo. If you do trying to hold the camera manually, you'll get some jitter that will blur the photo into oblivion.
Also learn to accept that most photos as you shoot them will need color balancing and post-processing. They will not be ready for your portfolio just as the camera saves them to the flash card. Make sure you've got some software you can do this in. I prefer Adobe Bridge and Photoshop because I can
knock out hundreds of photos in not a lot of time. If you go freeware into GIMP, you can usually make it work but it takes an extraordinarily longer time per photo and the results are a fraction of the quality you'd get out of proper
image processing software.