The first Saints Row is an Xbox 360 exclusive, sadly.

As Deepo said, the reason SR1 isn't available on Steam nor GOG is that it's an Xbox 360 exclusive. I haven't played the original game yet as I don't own an Xbox but indeed, story-wise not knowing the original game didn't feel like a big issue when I first played SR2. It's so abstract and humorous that I couldn't care less. Admittedly I would have enjoyed seeing how some of the characters were originally introduced but it didn't really make the sequels any less fun. And especially SR3 had such an extreme change in style over SR2 (and presumably SR1) that it almost felt like the start of a new series to me. Again, you could just as well start playing the series with SR3 and skip the original ones altogether, although personally I consider SR2 much better than SR3. Haven't tried the newest ones yet.

As someone who played the first and second game, just stick with the second game as the first entry into the franchise. The first game is good, but the problem is that it was more or less a slightly improved Grand Theft Auto: San Andreas clone which was cool at the time, but now it is just kinda meh compared to the second game. Second game still has the GTA clone feel but it has a lot more to offer to make it its own game.

That's a little disappointing but very informative, thanks everyone. I guess I'll just start playing as soon as I have the time.