Welcome! You are correct about it being a Sears. More specifically, a Murray-built Sears. So parts can be picked off Murray, Sears, or Western Flyer brand bikes. Now this is actually a Spaceliner. The hub on the chain ring gave it away. That was an exclusive piece for this model. It is nice to have the rack, but you are missing the light (or reflectors, whichever option it had). Both are hard to find. The rocket reflectors go for about $25 a piece, the light, about $40 just for the assembly. The lens itself (if you can find it!) would be about $70 easy and $50 for a reproduction. The bike could have one of two tank styles, either the older, more common style tank, or the "7 style" tank. The tanks would both have a horn, light, and a chrome dash board for the controls. The tanks for the womens frame bikes seem to be much marder find, I always end up with a men's tank.
I have a 1966 ladies frame, and only because it was an old family bike am I restoring it. But parts, time, and cash are holding me back.
In my opinon, these bikes are one of the coolest out there and are sign of the Space Race America was in at the time. Huffy also had their version, it was called the "Silver Jet" and they appear to be a bit harder to find than these. Even more rare is the Monark Silver King, it is basically a rebadged Silver Jet, but has different colors and a few exclusive items like badges, etc.