If you want the best battery life for your money, get a Canon.
I have a Canon PowerShot A 610 I use all the time and I’ve changed the batteries (AAs) in it twice in the year and change I’ve had it. I can probably get 800-1000 shots on a battery. It’s bigger, which cuts down on hand shake, great screen, good image management software, plays nice with my computer, 5 megapixels. Point and shoot modes for quick snapshots and options for more creative photography.
You read the reviews, look at the images posted from the reviewers, and read up on the specs. 
It’s hard for the layman to quantify lens quality, that’s why good reviewers take a standard set of shots under controlled conditions so you can compare. I use DCResrouce myself, and then view the images to see what I like and dislike. MP is measurable, but doesn’t tell you much of anything useful beyond the minimum.
Putting the Zeiss name on a lens from Sony doens’t mean much either, since Zeiss has essentially nothing to do with those lenses. Those are really Sony lenses, which are pretty good as well.
Wow. I have the PowerShot with 4.0 megapixels and 4X zoom, and I go through batteries (rechargeables) relatively quickly.
4.0 megapixels is fine for me but I am regretting not having more zoom; I’d like to snap the birds outside but can’t zoom in far enough to get real detail.
I’d recommend the Canon overall; I got it for $144 at B&H online and it does fine.
I’ve had an A610 for about 18 months, and have taken nearly 4,000 pictures with it. I don’t get as many pictures as 800 on a set of batteries, but it’s going to depend on various factors, including how much you use flash, and whether you use the LCD screen or the viewfinder to frame your pictures. (Both flash and the LCD screen use up electric power).
I thought 700 was a bit high. So I double-checked my camera and SD card.
It was a bit of a hassle, but I got my flatbed scanner to scan my camera’s LCD. I also scanned my SD memory card to be sure.
Check out the scans on Flickr:
LCD (regular scan and closeup)
SD card
My guess is that this Kodak model uses very lossy JPEG compression.
I still use my old A40 (2MP) quite a bit. Takes 4xAA batteries. I can do roughly 1000 pics per set of batteries, providing I use the kickass (and expensive) Energizer Photo Lithium AA’s (10€ for a pack of 2 in Germany - wayyyy less hassle than rechargables), and just use the viewfinder. Faster on burst mode too.
NB
I just bought my first digital camera and many of the same questions you do. I did tons of research and finally settled on the Canon A570. It was only $50 more than the cheapo digital but had a ton of features that can grow with me if I decide to get more involved in photography. It’s also very well reviewed, both on Amazon and on other camera sites, plus comes from a manufacturer known for good cameras. It’s not a tiny credit card sized camera but it’s fairly compact, could be easily slipped into a pocket and and I find the bulgy side thing (is there a name for that?) makes it easier to hold.
The other thing I concluded from my research is that most digital cameras nowdays are pretty good, compared with older ones and so even the cheapest ones would probably be OK for snapshots.