I'd build the Free Spirit myself, but would recommend starting with a cruiser frame- a modern lighter one, with alloy rims. I use alloy 700c and 27" x 1 1.4 rims myself with no problems, but I don't ride off road, and have 14 years of road racing in my distant past- so I'm comfortable with narrow tires, and believe me, the motors are too-
the bikes and wheels have caught up to the 50 cc motor,if you know how to build a frame that way.
Your Schwinn is probably mid-1960's, judging by the decals- pretty early- but women's frames are harder for a china build. Nice bike though.
I'd go with the free spirit- lose the front derailleur at least- I like to put a single freewheel on the back and match the chains, but the derailleur will work fine otherwise, with the advantage of being the chain tensioner- you may not have enough frame clearance on the motor side otherwise, and probably would have to use a tensioner there- I'd recommend this one, if you can afford it:
The only other problem with a diamond frame is that the top tube is a litle short and puts the tank in the way of normal peddling- if there's room you might want to play a small plastic tank hung under the top bar at the front-
there were under top tube steel tanks, but I don't think they've been stocked anywhere for a year or more-
good luck whatever you decide-
I like cruiser frames for clearance- you can still find them used cheaply- and I've eveolved to putting the light and narrow rims and tires on. You can build a cruiser and convert later- I started with just a 27 front wheel and a caliper brake- skinny and light and fast rolling, like a chopper motorcycle.
If you find the serial number on the schwinn racer, you might be able to search the year online