If you can mount a caliper brake for the front wheel (does the fork have a hole in the crown for one?) then I'd just rebuild the front wheel with a new rim and leave the rear wheel alone. Most of your braking power comes from the front wheel so a decent brake there even if combined with a mediocre one in the back should be fine.

If the spokes are in good shape you may even be able to reuse those provided the new rim has an ERD (eff. rim diam.) that's close to the same as the current rim. I've replaced rims by taping the new one alongside the old one and then moving the spokes over one at a time before finishing the wheel build and truing.

Chromed steel rims work fine for braking when it's dry, but are terrible when they get even a little wet. So I'd use an aluminum rim for your wheel rebuild.