+1 Start hitting the thrift stores and garage sales. I have found many bikes better than a Varsity this way for less than $25. Then sell your current Varsity to fund the acquisition.

The harder you look, the better deal you will find.

French bikes are more trouble to refurbish. I would look for either one of the better US brands like Trek or a vintage Japanese bike.

There is no reason to spend $200 on a Walmart bike when you can find something a lot better for a lot less (if you are willing and able to spend time looking).

I also found a like new training stand at a thrift shop for $5.