I got into straight razor shaving via double-edge shaving. I've been wetshaving (using mug and brush) since college. I got into DE's as a cheaper way (that's what I thought until I learned about the various AD's...and I still wager that I would have spent more in Mach3 cartridges than I have shaving gear in the last 3 years) to shave, and most certainly a more environmentally friendly way to shave (no plastic!). I also like it because it is not just another mindless activity, but requires some skill. After nearly 3 years of shaving with DE razors, I got interested in taking the next step and gave straight razor shaving a try. Besides that, there is just something about shaving with an extremely sharp piece of steel without filleting my face that I find very satisfying!
With a DE, I can get a 3-pass shave done in under 10 minutes (around 3 if I take the chance for irritation). I'm shaving in about 10 minutes with a straight, but I expect that time to improve with practice.