Hello bike forum community! I waited way to long to turn to you guys for help. I'm currently fixing up my bike for the school year and noticed I need a new rear wheel (it's the screw that goes through the middle it gets kinda tough to turn at times and the rear cassette is stuck on and requires a 24 spline tool to remove it, which isn't that common I guess). My bike is an early 80's Schwinn Varsity so I'm assuming it will fit 26 by 1 3/8ths inch wheel but I'm not 100% sure. I was looking at this wheel I saw on amazon:

Sta-Tru Silver Steel 6-7 Speed Freewheel Hub Rear Wheel (26X1 3/8-Inch)

and was wondering if it would work for me. I'm trying to save money so the cheaper the better (I know that's very often wrong). I was also wondering if this wheel is compatible with a rear freewheel cog I bought "Diamondback BMX Freewheel 3/32" 16T". I'm sorry about sounding stupid but my knowledge seems much more limited than I expected.

Thanks in advance for any responses (even if it is someone saying, "You're waisting you time on an old heavy varsity just buy a new bike")