Your photo shows a single pivot caliper brake. The main measurement is how much "reach" it has from the single mounting bolt down to the brake pads and represents a range.
Any replacement caliper needs the same reach to get pads to the rim track.
The other variable is the bolt - older bikes use a threaded post which has a clearly visible hex nut on the rear side.
More modern brakes tend to have a recessed threaded "nut" with a hex socket. These might be described as "half of a Chicago nut/bolt set"
As for your options, the single best fix for any brake is to replace the pads with something more modern. The rubber compounds harden and oxidise with age and UV, and performance drops. Koolstop have excellent options - your bike might take road cartridge shoes with replaceable brake pads.
Second is to replace the brake cables, both inner and outers. They degrade over time and add friction. Check first that you can get an inner cable that matches your existing brake levers. There are multiple common standards as well as other rare ones.
Third is strip, clean, lube, and reassemble the brake. It should have buttery-smoothness when you press the two pad-arms together by hand. Do take photos as you disassemble, and use a lubricant like white lithium grease.
Finally - if you can find a dual-pivot brake caliper with the right reach and same mounting bolt, then it could be a useful upgrade on the front of your bike. The brake at the back doesn't contribute very much to braking effort, so there's less gain by uprating it.
Here's a longer-reach dual pivot brake, but the bolt at the back probably doesn't match your mounting.