Those are tricky questions.
I've primarily played my first playthroughs of the games solo, and I've really enjoyed the experiences. They're engaging enough, and although the side missions in the earlier games could get a bit "collect five bear asses"-y, I still found myself trying to complete everything. The games can be remarkably chill when you're just puttering around. From a gameplay perspective you're probably good to jump in with 3, especially because it seems to be a bit more mechanically up-to-date.
Story-wise, I'd probably recommend playing the previous games. Borderlands seems to be very additive, with each new game building up and fleshing out the playable characters from the previous games. A lot of the moments in Borderlands 2 wouldn't have had the same punch if I hadn't played Borderlands 1, for example. If you don't have that connection with the story so far, and the characters, the game will probably just come off as a series of crude jokes.
So, long story short, if you have the time, are okay with some less-refined gameplay, and are invested in the story, I'd say play 'em from the beginning.