One way around stripping the paint completely is to sand everything until all chips and dings are completely feathered at the edges, and all rust is removed. And do sand the entire surface, just not necessarily to remove all the paint. Sanding will help with adhesion, the old paint should not appear shiny anywhere after you sand.

Clean all the dust off, then use a liquid sander (aka liquid deglosser) to wipe the entire frame down. Following the directions on the liquid sander can, you'll be instructed to prime within about an hour of wiping on the liquid deglosser in order to get maximum adhesion. Prime the entire frame with a couple of coats of primer. Additives in the liquid sander will make the primer stick to the point that you would need a chisel to scrape it off once the primer has cured.

Sand the whole frame lightly with very fine sandpaper to knock down the primer, clean all dust off, and you're ready for two or three coats of color, and then clearcoat if applicable. Wear gloves and work outside with the liquid sander, it's nasty, toxic stuff. But it works great, we used it extensively when I was a painter for about ten years, when adhesion was an issue.

Like Retro Grouch says, rattlecan jobs can produce decent results, not factory quality, but decent. I've got rattlecan paint jobs that have held up extremely well, and folks are always very surprised to find out the paint came out of a rattlecan-