The most popular balloon used in twisting is the 260.  The 260 is 2" around & 60" long when fully inflated.  Although quite often the balloon is not inflated fully (depending on your creation), it is important to recognize the size.  The 260 is also known as a pencil balloon.

The 160 is 1" around & 60" long when fully inflated.  It is also known as a spaghetti balloon.  Used for smaller creations & details.

The 350 is 3" around & 50" long when fully inflated.  Used for larger creations & bodies of characters.

The 646 is 6" around & 46" long when fully inflated.  You probably won't need this balloon right off the bat.  It is used in more advanced creations & not a very easy balloon to work with.

The 321 is 3" around & 21" long when fully inflated.  You'll notice this balloon has a colored "tip" on the end.  This balloon is usually referred to as a Bee Body.  It's best known for making bug bodies, but has quite a variety of uses.  You'll find this a good balloon to have on hand.

The 6" heart is probably the second most popular balloon, right after the 260.  It inflates into a heart shape without any manipulation from the twister.  Ideal for flowers, wishing wands, butterflies, fish, and a multitude of other things.  If I could only have 2 types of balloons, they would be the 260s & 6" hearts.

The 5" round is very useful for eyes & details.  You can get them plain or imprinted with a variety of 'faces'.  Consider using Alien Heads, Pooh Faces, Spiderman, Eyeballs, Friendly Eyeballs, Google Eyes, Frog Faces, Bird Faces, etc.  These can really make your life as a twister a lot simpler. 

Another balloon you might find useful, you might also find a little expensive.  The 6" GEO Blossom is a great way to make flowers, collars for heads (see 5" rounds), and a few other things.  They are very pretty, but some find them difficult to tie, and they do cost a good bit more than other balloons.  Save these for special occasions & advanced creations.