You want to make sure you get an edition that has the original illustrations by John Tenniel. A few minutes poking around on Amazon suggests that the
Bantam Classics edition contains all the original illustrations and is a bargain at $4 new. I saw some of the comments mentioned that the Kindle edition is missing the illustrations and doesn't have proper formatting of the poetry, so you probably want to grab a print copy at the moment.
If you enjoy Alice in Wonderland and Through the Looking Glass, I'd suggest you revisit them at some point in the future with Martin Gardner's wonderful
annotated edition, which provides a ton of historical detail, period references, and even some explanations of some of the more esoteric gags. I wouldn't recommend starting with this edition for your first reading, but if you're intrigued and would like to know, there you go.
FnordChan in NeoGAF Land