I have a hand-me-down Craftsman circular saw that is probably from the 1970s. It mostly works fine, but makes a grinding wheezing noise when decelerating after power has been cut (finger taken off trigger). Knowing my dad, if there were multiple 7 1/4" Craftsman saws available at the time, this was the cheapest one. Is it wiser to just replace it, or is it worth repairing? If it's time to replace it, what are your thoughts on corded vs. battery?
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.
Chances are either 1) the brushes are shot, in which case it may be a cheap fix, or 2) the motor itself (bearings, windings) is just wearing out. In the latter case it's probably not worth the cost and effort to have a repaired very old saw.
As to what you should buy, I have no idea what your needs are. I like Makita 5007 corded saws. A number of brands make nice Lithium cordless saws.