Should I repair or replace a wheezing circular saw?
Repairing small hand tools is rarely economically feasible (even thought the thought of built in obsolescence/landfill overload is distressing). 

It sounds like a bad bearing, but the cost of the labor involved in changing would probably exceed the cost of a new saw.

I would get a new one.

Cordless tools are great, even in a shop. But circular saws need a good deal of power, and most cordless ones are seriously underpowered. Unless you will be away from outlets a good deal or limited to a few cuts in light materials, I would opt for a corded circular saw.