I usually leave the old paint in place, patch any dents, and re-prime.

Bix paint stripper will remove that old lead paint - if you feel you must.

I recently used this on a High Speed:
http://www.lowes.com/pd/Jasco-17-oz-Liquid-Multi-Surface-Paint-Remover/3562712
It was the third or fourth thing I tried, as the citrus gels and brush-on strippers didn't have much effect on the paint.
Spray on lightly, wait a few minutes, then scrape. Do a small section at a time, as you don't want it to dry or soak into the wood. Used lightly, it'll do just enough to take off the top 'shiny' layer of the paint so that sandpaper will 'bite in' instead of skimming across the surface of the paint.