Well I decided the Raliegh was worth making a road bike out of. I'll keep the heavier Supercycle for the trails (I'll get more exercise that way).
Upon investigation the chain was worn, and had one stiff link. It is soaking in oil. But I found that when I have it in 1st and have all my weight on the front pedal and am pulling up on the handlebars with a force about equal to my weight, the bike decides to shift into second gear:. Why is it doing this?