Your radio likely will need capacitors, especially those in the power supply. If the radio doesn't work, or if it hums, replace capacitors first. Believe it or not, the capacitors are more likely to be bad than the tubes.Tubes aren't usually very expensive for these old radios, so you might buy a set. If one of your tubes is bad, you can swap them one at a time to find out which one it is. Put the originals back in one at a time to see which ones work, and keep them. Tubes last a long time, so don't throw them away unless you're sure they're bad.
If your radio has wiring with rubber insulation, replace with cloth. You can get a spool of this kind of wiring, as well as tubes and other parts at Antique Electronic Supply. Also check BOIAudioworks for tubes.