[morzh]

Either 18 or 20 gauge is fine, the currents in tube radios are very small and any of these have 10-fold ampacity.
I would use 18 only for tube filaments wiring, and even this only for the rectifier tube filament, unless you have many tubes in parallel (in radios with lots of tubes more than one winding is used so the current is split).
In your case all tubes are in parallel, so maybe 18 gauge for the filaments. Though it is for the peace of mind, 20 will do just fine.

Either solid or stranded are fine but stranded is forgiving when you bend it back and forth many times whereas solid might break.