Batteries:

I have cameras with Lithium and AA type batteries.
And batteries that charge in the camera and out of the camera.
To me, the battery type is a "don't care".
Why limit you camera selection based on the battery?

Megapixels:

Cameras are available all the way up to and including 12 megapixels.
This year the most common on new cameras is 7 megapixels. Which is large enough for over 95% of all photographers.

More megapixels are good if you are planning on printing very large photographs.
More megapixels are good if you do a lot of cropping of photographs.
If you are into making slide shows from photographs, more megapixels means that you can zoom into the photo further.

Camera Software:

Most software provided by camera makers is adequate, but none compare to a program like Adobe PhotoShop Elements.
If you are looking for easy......look at the free program Irfanview.

xD picture card:

xD picture cards are co-designed by Fujifilm and Olympus, although neither company actually manufacture them. All present Fujifilm and Olympus cameras use xD picture cards.
No other camera company uses xD.

The very newest Fujifilm cameras can use xD and SD cards.

Red-eye:

Red-eye if the curse of the digital camera.
Red-eye is caused by the close placement of the lens and flash bulb.
The red-eye setting for flash seldom works and often causes people to shut their eyes. It also slows down the flash cycle.

Some cameras claim to automatically fix red-eye in the camera.
Some will let you fix the red-eye when reviewing the photos in the camera.
There is also excellent red-eye removal software.

Shaky Hands.

Camera movement is the usual reason for blurred photographs.
Small lightweight cameras contribute to this.
...(a large medium weight camera is much easier to hold steady)
Shooting in low light (without flash) is also a cause because the shutter speed is too slow in low light.

The LCD is also a contributor to blurred photos.
Using a viewfinder and holding the camera against your head is much steadier that two outstretched arms while using a LCD.
Your head is much steadier.

Price range:

Most people have a maximum amount they want to spend on a camera.
If you maximum is over $600, you should be considering a DSLR (digital single lens reflex) camera.

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