Version 2 (AKA 2nd Edition) was superseded by Version 2.2
Main differences are that Ver. 2 uses a d10 system while Ver. 2.2 changed that to a d20 system compatible with the Traveller: The New Era (AKA Traveller:TNE or just TNE) rules. This also means that material for TNE is compatible with Version 2.2.
1st Edition (AKA Version 1) uses a percentile system and in some cases has more complex rules mechanics than Ver. 2/Ver. 2.2 which is why some people prefer the later editions. Some of us prefer the easier rules because they're quicker to implement. To me,
this is the most important question you need to answer - are you and your friends interested in complex rules or do you all prefer less complex rules.
Personally I prefer rules light, I'd rather have a good story that the rules guide and assist with, rather than a heavy/crunchy set of rules that force the story to conform to the reality created by the mechanics of the game.
2nd Ed and 2.2 both uses a Difficulty Level system to judge the success or failure of a skill check. In 2nd Ed. this is a three level system consisting of (if I can remember properly) Easy, Difficult and Impossible levels of tasks. In 2.2 this was increased to five levels of difficulty - Easy, Average, Difficult, Formidable and Impossible (Impossible does not literally mean impossible, just that the task is incredibly difficult).
Both systems work on the idea that Difficult requires you to roll less than or equal to your relevant skill to pass the check. For 2nd Ed. Easy requires you to roll equal/less than 2x your skill and Impossible requires you to roll equal/less than half of your skill to pass.
For Version 2.2, the old Easy is now Average and the old Impossible is now Formidable while the new Easy has become 4x your skill and the new Impossible has become 1/4 of your skill.
The 2.2 system allows for a greater range of checks and the rules also mention that you can expand this further if you need to by for example including 8x your skill for really easy tasks that still have a chance of failure and also 1/8 your skill for really difficult tasks that still have a slim chance of success.
It's worth keeping in mind that the 1st Ed. scenarios can be adapted to 2.2 rules without much difficulty so it's definitely worth thinking about buying them if you want lots of adventure/source material.
And yes, there was a Version 2.1 but it was a more of a test of updating the Ver. 2 mechanics to a d20 system. They refined/improved it and created the 2.2 system from the information.
All the 2nd Ed. material is compatible with the Ver. 2.2 system, you'll just need to be aware that some tweaks might need to be made
This also means that any material from the Dark Conspiracy 1st Ed. and Cadillacs & Dinosaurs game is able to be used because they share the same rules system as T2k 2nd Ed.
Dark Conspiracy 2nd Ed. is also compatible with T2k 2.2 because their rules systems are practically the same (with just some minor variations such as the rules governing vehicle travel).
I would recommend you either buy a bundle from DriveThruRPG or buy the CD-ROMs from Far Future Enterprises (AKA FFE). The CDs are available as one CD for 1st Ed. and one CD for Version 2/2.2, however they include everything released for their respective editions. The CDs sell for US$35 and are much better value for money but you will have to wait for delivery (keeping in mind that FFE is basically a one-man operation consisting of Marc Miller and whatever friends or family he can get help from).
The hardcopy would be nice to have but you'll spend less money printing the various pages from the PDFs you'll need... but, the hardcopy would be really nice to have (I have the CD-ROMs but I still like to have the physical books at the game!)
FFE
http://www.farfuture.net/cdroms.html
DTRPG
http://rpg.drivethrustuff.com/browse.php?cPath=23