In digital cameras, you'll need to know what your going to use it for.
If you're going to make hard copy pictures, e-mail, or desk top stuff.... ? That will determine the number of pixels you'll need. 3 megapixels (MP) is good enough for up to 4X6 hard copies. But if you want a 8X10 you'll need 6MP or more. Although I did make a 8X10 on a 3.3 MP camera and it came out great. But thay's not the general rule.
Is it going to be a pocket camera (which most are) or can you go with one that's not small enough to fit in your pocket? If you need a camera with a long lense, larger than 3X (or about 120 mm) you'll proably have to go with one that's not pocket size.
And as Jeff Lange said, digital zoom is useless. You can crop your picture and get the same results as a digital zoom.
And long lenses are not that hard to use. You just need to keep it steady. Hold the camera in your hand and support your hand on something fixed like a rail or siton the ground and use your knees, or just use a tripod. That's where good technique comes into play. There is no substitute for a long lense if you need to take a close up or a photo at a distance. Lense quality is also important, but in a $300 camera, you're not going to get much choice.
A good website to look at cameras is:
http://www.bhphotovideo.com/
or
http://www.17photo.com/
They're not the cheapest, but they have competitive prices and they are legit on line photo sites.
If your really on a tight budget, try to find a camera that uses Secure Digial (SD) or Compact Flash (CF) memory cards. Your going to need to get larger memory cards and the CF and SD cards are cheaper than the tiny XD some of the others. Also look at the batteries. If you can find a camera that uses AA batteries instead of the special battery packs you'll be better off. You can get real advanced rechargeable AA batteries that will by far out last the battery packs at a reasonable price and still have backup batteries. You should always have a backup battery.
Thats my take on digital cameras.