Basically, for the connection there are wired and wireless. The wired type has 2 sub-types: the USB and PS2. The wireless are using 2.4 or 2.8GHz frequency. Some wireless mouse even use bluetooth connection.
As for the mouse type itself, there are track ball and optical. I heard they use laser now. That's all I know about that particular accessory. Personally, it's a non-issue whether it's wired or not, as long as it's not trackball.
Just to add a little to Damasvara's excellent description, and to pre-empt his question...
The price of a pc mouse varies widely. From $1 to hundreds. What you need to ask yourself about peripherals is what is the added benefit of having a more expensive mouse.
I would avoid track ball and go optical. They are even cheaper now, and are much more reliable and accurate.
Wired is better for gaming (IMHO) as it doesn't require batteries, can't recieve interference etc. So you won't get fraged becuase your phone recieved a text and your mouse went mental...But if you are using your pc as a home cinema then it can be nice to sit on the sofa and hit play, so wireless is nice. Don't forget, good batteries are a good investement with a wireless mouse, alternatively, pay a little more for a rechargable mouse. :-D
As for makes and models, stick to your budget and buy the best you can within it. I have a Razor, but Logitech are great too.
Also, a step above optical is laser. Not necessarily more expensive but it has better resolution so it's smoother.
I bought a very simple combo from logitech, the EasyCall desktop ($180). It comes with a USB speakerphone, a headset, a wireless keyboard with some nice features, and a wireless laser mouse with 5+ buttons (depending how you count them lol). It's been very good in gaming, very accurate.
Batteries aren't a big issue, I bought some cheapo pack. They keyboard has run out twice, and the mouse is just now reporting being low, and I've used them since April.