I switched to clipless a few months ago when I bought my new bike. I don't think I'll ever go back.

If you're looking for improved speed, as you mention, then clipless pedals are the way to go. You will fall over at least once as you are learning, but you can set the tension so that it's no more difficult to unclip than to take your foot off the pedal; you just need to move your foot differently.
As for stop-and-go riding, you can definitely do it. I became most familiar with my clipless pedals by riding in stop-and-go traffic. Ride for 30 seconds, unclip, wait, clip in, ride again, etc. It becomes an automatic motion.
If you want to have all the benefits of clipless pedals and also the benefits of flat pedals, you can get pedals that can be used either way, or you can buy "tennis shoe adapters" (e.g.
Nashbar Tennis Shoe Adapter ) . I've never tried them, but they seem like a good compromise.
Tim