Batteries:
General:
http://www.livingroom.org.au/photolo..._batteries.php http://www.digitalcamera-hq.com/hqguides/batteries.html
Detailed info:
http://www.imaging-resource.com/ACCS/BATTS/BATTS.HTM
In short - Lithium ion batteries don't have the memory effect (though that does not mean they don't "degrade" with time). However, they are more expensive and you need a spare anyway - no particular indication that they don't deliver "the juice". Also, you'll not be throwing away any of these for a while, so there is an environmental consideration as well (?). I've not had any problems with mine, but you do have to plan your photo trips to be sure you're all charged up.
AA is a good option for travel etc. for reasons you already stated, but if you're thinking about just using alkaline batteries then you'll run into problems because they don't deliver sufficient power to last very long. You will still need to buy a charger with a set of rechargable NiMH batteries (refer to second and third link) as your "primary" power source. Backup sets also required here - but cheaper than lithium ion - though with memory effect.
Check that the camera you want to buy can use specific battery types.2
Megapixels
As for megapixel resolutions, personally I'm more concerned with the optical zoom of a camera. As far as I can recall, the Mars lander probes were fitted with 1 MP cameras - however, they had great lenses fitted. In my mind, megapixels = print quality, while optical zoom = photo quality (in most cases). For general picture taking (which is what you seem to want it for), I'd go for a middle range one - 5 MP is more than sufficient, and you can use the difference in price to get some other features - stability control, lenses, etc. - maybe try to get one with optical zoom greater than x3 - though these get bulkier in general, so figure out what you're happy with lugging about. I think you'll have a more rewarding digital camera experience that way instead of just going for the "megapixels".