It was partially recapped, but how well, and when? That electrolytic under the chassis should be a top mount, but was cobbled in. That's a sample of how careful the recapping was. If there's a dead 'lytic up top now, you can leave it for visual effect and add new ones under the chassis. Probably need some terminal strips.
You should stick close to the values on the schematic. Too large a first electrolytic filter can overstress the rectifier tube on startup as it tries to fill up that big empty cap with juice, just what you want to avoid. You could use a 10mfd for the first cap out of the rectifier, and a 22 for the other two electrolytics. Voltages should be at least the same as the schematic or a little higher.
After checking it over and changing the 'lytics, you could probably make it play, but for peace of mind and neatness, it would be cheap to just go ahead and recap it per the schematic.
As to fuses, you can (or could not too long ago?) get little clip-in fuse holders from RS that you just solder in under the chassis. For the line you could try 1.25 amps. The heater draws 0.6 amp so a 0.75 or even 1.0 amp would be OK. The maximum B+ rating of the 6X5 is 0.75Ma, so a 100Ma (1/10 amp) fuse would work. All the fuses need to be rated for the voltage they will see, or more.
You can get even more peace of mind (how much do you want??)
by installing an NTC (Negative Temperature Coefficient) thermistor in the transformer primary circuit. This has a high resistance when cold, but the resistance drops to a negligible number quickly, allowing full power. So you get a soft-start effect for the whole set. A good one to use is a CL90, 120 ohms cold, 2 amps max. This type could be used on most radios. Resistance is only a couple of ohms when hot. Mouser and others sell them.
That'll be quite a radio when done!
Reece