Typically, the cameras that use AA batteries are going to be larger than one that uses a rechargeable lithium. Usually (but not always) the larger cameras have a better optical zoom range. Ignore digital zoom when shopping for a camera, optical zoom is the one that counts. If you do buy a camera that uses AA's, you'll want to invest in rechargeable AA batteries for it, because digital camera eat regular alkaline batteries like crazy.
I like Canon's and I've owned a couple of them. But, my favorite camera by far (other than my large DSLR) is my Panasonic Lumix. It's fairly small but not tiny, has a huge LCD screen, and has a 12x optical zoom (which is practically unheard of in a smaller camera). It's great for getting those far away shots. It uses a rechargeable lithium battery, and I've went thru a day of taking over 500 pictures and it didn't die on me. It also has excellent HD video capability. You can simply use the "auto" setting, or you can click a couple of buttons and have various setting like nighttime, fireworks, sunset, sports, beach, etc. The camera has a Lumix lens, which is highly regarded as one of the best out there for picture quality. My version of the camera is almost 2 years old, but here's a newer version of it on
Amazon. It's selling for $238 at the moment for the silver color. I think the red and blue are a few bucks more.
http://www.amazon.com/gp/product/B001QFZMD8/ref=noref?ie=UTF8&s=photo
edit: LOL, me and the poster above me just recommended almost the same camera. The only difference is that the LCD screen on the one I mentioned is slightly larger. Either would be a great choice.