If you are a true (or nearly) neophyte and have bought nothing yet I'd say get the basics for CT. Either pick up a copy of one of the following packages (just one of, they are all essentially the same):
1 - The Traveller Book, a compilation of the original basic rules in one volume, hardbound or softcover. Often avaialable on eBay.
2 - The original Little Black Books (LBBs) 1-3 (and optionally 0, 4, 5, 6 and 7 though not needed). Also looking on eBay is the best bet.
3 - The FFE reprint of LBB 0-8 "The Classic Books". Not sure it's still in print or not, check here (but drop an email before ordering):
http://www.farfuture.net/ffe/n9000.html
4 - The QLI compilation of LBB 1-3 available for order through here:
http://www.travellerrpg.com/cgi-bin/catalog/pview.pl?action=view&stocknum=ffe000&h=header_catalog&s=
Any one of those should give you a good feel and taste for the game, and if you don't like it they should fetch fair resale.
Compatibility?
Well, CT grew over time and that became compiled with much errata as MegaTraveller. It's sometimes available on eBay but there is supposed to still be a CD pdf version in the works. The two are in the same spirit but very different in play from CT LBB 1-3 to MT. CT with all the supplements and journals and ??? would be very close to MT.
T20 is probably closer to CT in some ways than MT and further in others.
If I could have my mind wiped of all Traveller knowledge and were to start again I'd go with LBBs 1-3 in some form (preferably The Traveller Book) and have a post-hypnotic suggestion implanted to make me blind and deaf to every other bit of Traveller ever printed or spoken