Like James_S said, replace the caps. All of the electrolytics will certainly be dry by now. Also, the paper/foil caps that were dipped in bee's wax have changed in value. Replace all of the caps, without exception.
The resistors may also have changed in value. Check and replace any that have drifted high in value.
Don't spend money on tubes until the caps and resistors have been replaced, and you have tested the radio out. Chances are, most or all of the tubes are fine.
If you haven't already tried to power up the radio, DON'T. As a minimum, replace the electrolytics in the power supply first, then bring up the AC very slowly, with a variac. If you don't have a variac, build a "dim bulb" tester. A 1930's radio almost certainly had a power transformer. You risk burning it out.Also, look closely at the wiring before applying power. If cloth covered, it may be OK. If plastic, it will probably crumble at a touch.
Speaking of plastics, other than bakelite, the few plastics of the day will have shrunk, cracked and yellowed by now. If you have bakelite or wood that is in good condition, that's one less problem. Be aware that some manufacturers used a very thin veneer over a cheaper wood (Philco was guilty of this, among others). The veneer is very easy to damage.
Depending on how much effort you want to put into keeping the radio looking "authentic", you could spend much more effort. One of the radios that I had was a 1932 Philco cathedral radio. The paper caps were inside little bakelite "bathtubs", and potted with tar. I replaced the paper caps with modern pollys (I didn't replace the tar). When re-mounted, you couldn't see the substitution. For the electrolytics, I cut open the nickel-plated copper can, soldered a new part inside, then re-sealed the can. When re-mounted, you couldn't tell it was modded.
Unless you want to get obsessive, I'd say, if it is underneath the chassis, and won't be seen, use modern parts and don't worry about the looks.
You can find lots of info and get help on
www.antiqueradios.com. Years ago, there was a guy on there who specialized in selling radio knobs. I bought several. I haven't been on that forum in quite some time, so I don't know if he is still around.
Things like dial string, dial light bulbs, replacement speaker grill cloth, replacement cloth covered wire, etc. can all be found from various vendors.
One last thing. If your radio is a US model, PM me the make/model, and your email address
. I probably have a schematic and alignment instructions.