OP:
Which should I buy?

wrote:
If the Schwinn has a frame mounted derailleur go that
way you won't regret it.

What difference could it make? Bikes of that genre have
nice functional $14.95 rear derailleurs. If you should
happen to damage one or wear it out, they are readily
available. Even upgrade models at $20 and $25 . Of all
the factors I can think of, this is among the least important.

Get one that fits. Open bearing assemblies, grease them and
adjust properly. Spend a bit of time lubricating and
adjusting the brake and gear systems. Tension the wheels and
ride it.

--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971