John,
No question the best parts source for your Zenith is AES:
http://www.tubesandmore.com/
It is my understanding that the rectifier changes alternating current (ac) into positive (+ only) current, so that's a pretty important step in basic radio function, I would think.
The fried cap on the power line could be the result of line surge or peaking, so heed Chad's tip and splice in an inline fuse. Cheap insurance to prevent it from happening again.
Power transformers are pretty sturdy and basic, but leaky or old caps can do them in. I'd suggest running power through an isolation transformer after the recap and bring the voltage up slowly. Hopefully, it'll all work out and you can get on with the business of enjoying your Zenith as intended.