For The Absolute Beginners Yoyo- A Good Yoyo Just to get The Feel for it - self winding Yoyo.
 
Choose between types of yo-yos. Since yo-yos have been around for literally thousands of years (they've changed a bit since ancient Greece), a few different kinds have emerged that serve slightly different purposes:
Imperial yo-yos. This is your classic, circular shape. These are for "looping tricks" -- where the yo-yo isn't sleeping but routinely coming back to your hand as you make loops and circles with the string.
Butterfly yo-yos. These are shaped just like their name -- larger on the outside, smaller on the inside (like wings). They're good for string tricks, where the yo-yoist creates intricate, woven webs with the string.
Automatic yo-yos. Yomega quite a few years back started the craze of automatic yo-yos: ones that could "sleep" (stay on the bottom of the string, spinning) and "wake up" (come back to your hand) on their own. These are fine, but it's kind of like cheating. If you want to actually do your own tricks, you don't want an automatic yo-yo.
Off-string yo-yos. They're literally that -- off the string. It's technically a yo-yo but it's more like an awesome grooved disc that bounces on a string as you manipulate. It's generally reserved for very serious, competitive yo-yoists.