Shadowrun has had five editions. SR1-3 was a relatively smooth progression. SR3 is the best out of that set. It has a lot of good features, but is also pretty complex, with lots of subsystems for things. With SR4, they drastically revised and, in some cases, simplified the mechanics. SR3 and SR4 are good choices if you want a game edition where all of the books are out, and where the rules have gone through eratta (and had a lot of people post house rules for them). They are stable, complete, functional games - and you can probably find a lot of the books used.
SR5 is another drastic revision, although not as drastic as the move from SR3 to SR4 was. It improves some areas, implements some other ideas poorly, and suffers from serious editing issues (although that is starting to improve). It is not complete by any means, but what I would consider the main supplements seem to be out (a guns/gear/combat rules book, a magic book, and a book of advanced character options). The advantage to SR5 is that it is the current edition, the one that will usually be discussed online. The downside is that it still has a lot of areas that need to be fixed.
