Since it's $.02 time ...
CT: Everything is based on 2d6. The system is wide open for GM interpretation. Skills are key, but they work largely however the GM wants them to according to the situation. The game is relatively simple and straightforward, calls for a fair degree of GM interpretation and adaptation, and plays quickly if the GM is light on his feet. An inexperienced GM can rapidly founder. Combat is simple but tends to fall apart at the extremes (heavy weapons or armor). Has tons of excellent support material, if you can find it.
MT: Smooths out many of the wrinkles of CT but adds complexity -- and wrinkles -- of its own. Still based on 2d6. There's a lot more structure to skills and combat, which helps the new GM but also means everyone needs to learn more in order to play. Personal combat makes more sense but is still rather unsatisfying in play. Best character generation rules of all versions, IMO (and they mesh perfectly with the CT rules, too). If you're not comfortable "winging it" but you still want that classic game ambience, this is a good choice.
2300: A complete departure from what came before. Everything's based on a d10 instead of 2d6. Everything basically works, too, including personal combat, which is another departure from previous rules. Much grittier and "hard" than before. The science is less hand-wavy and more interesting because of it, IMO. The universe is considerably smaller. Even though 2300 is more fundamentally sound in terms of game design, in most ways, it doesn't feel like Traveller (because in most ways, it's not).
Marc Miller's Traveller: A big disappointment to me; YMMV. The rules for event resolution put too much emphasis on basic stats and not enough on skills, so for me, they just don't work. Uses a varying number of d6s depending on stats, including half-dice. I know a lot of people who own this (some of the reference books are excellent) but not a single person who's actually played more than one session.
T20: If you know the d20 system, you pretty much know this game. If you like the d20 system, you may like this a lot. But like 2300, it doesn't really feel like Traveller, or not to me, anyway.
Gurps Traveller: Based on 3d6 instead of 2d6. Has all the strengths and weaknesses of Gurps. Character generation takes a long time but is rather fascinating and allows just about any sort of character imaginable. Actual play can be exasperating, however, especially when combat rolls around, because the game allows too much detail. Lots of scaling problems (again, IMO) in that the game tries to encompass too many things on one scale.
Mongoose Traveller: A return to a classic Traveller feel with a 21st-century emphasis on the 'unified mechanic' (good ol' 2d6 again but with standard modifiers despite the situation). If you prefer a one-size-fits-all method for resolving everything rather than CT's seat-of-the-GM's-pants approach, then MgT is a pretty good choice. ("One rule to ring them all" has its strengths as a game design philosophy, but like anything, there are cases where it falls apart. You just need to know what those cases are. That's true with any set of open-ended RPG rules.) MgT has a fair number of inconsistencies and omissions, as do every edition of Traveller, but the company supports the game well, it's nearly as simple and accessible as CT, and it's in print, a factor that shouldn't be underestimated. Honestly, if I was just getting into Traveller now and didn't have two bookshelves filled with 35 years of backlogged material, this would be my choice.
Steve