Though I wouldn't recommend it, you should probably be OK going straight into season 2. The way it starts is something of a soft reboot anyway, so you should get caught up fairly quickly.
Unfortunately one of the major mysteries of the first season ("why did the Minbari surrender at the battle of the line?") gets pretty much laid out within the first two or three episodes. That may somewhat hinder your enjoyment of season one if/when you get around to watching it later. It might also dampen the resonance of some future revelations as you won't have experienced all the groundwork from S1.
Honestly, I'd advise tracking down a way to view the first season by some other means if at all possible. I know it used to be on Hulu, so you might still find it there or some other streaming or rental service like Netflix, LoveFilm etc.