Thanks for the photos.
Firstly, I had another look at the schematic (assuming it's the right one). There's 5x type 27 tube, which you can still buy online for about $15 each. The first 4 are straight RF amps, and the last is what I believe is called the anode-bend detector (it's really ancient technology that soon fell out of favour). The last 2 tubes are type 45 which are rather more expensive, $70 or more (or a lot more), wired as a push-pull audio output stage. The speaker transformer (probably part of the speaker assembly) converts the valve's high voltage low current to the speaker's need for low voltage high current. Every valve radio has a speaker transformer, although the rest of the technology evolved over time.
As for the power supply, if it's an AC type (plugs into the wall socket), there will be a transformer, a rectifier valve (most likely type 80), some smoothing capacitors (which will need replacing), and perhaps a choke. Most radios of that age didn't have a choke, but instead used a winding on the speaker for that purpose. That's because magnet technology wasn't up to speed back then, and the magnetic field of the choke winding did the job instead.
If the power supply is a battery type, then all that's in there will be various batteries, all gone flat or leaking by now.
However, if we once again depend on the schematic, voltages exceeding 300 volts are mentioned, and these would only come from an AC supply. You can imagine what 300 volts would do to old dud capacitors. That's why you should replace all of them before even thinking about applying power.