If the cable is new it oughta be good for a while yet.
Make sure the Tektro caliper is compatible with the brake reach in your fork. Sheldon says how to measure reach. Yes that caliper should work great if it fits.
If you swap out your steel rims for aluminum, at least in front, that will be a very noticeable braking upgrade though certainly more expensive than a caliper. Used front wheels can be had for cheap at sports consignment stores, though it might be harder to find one if your record is set up for 27 inch wheels.