I hope you understand the dangers of working on valve circuits. Dangerous voltages are present, the sort that kill you!
They can even be there after switch off- stored in capacitors. It hurts, take it from me.
It will be simple to swap out all the old caps and flying blind, that can solve a host of problems.
If you value your project and self respect do try to re-form electrolytic caps.
Replace old wiring and put heat resistant sleeving on wires that go near the hot stuff.
Tubes may light but can still be faulty- try to get them tested or replace like for like.
Old resistors can have drifted way off value- test them. Dodgy resistors can kill your precious valves
The radio section will probably need some adjustments. To get this right you need a fair bit of RF competence an RF signal generator and a scope.
Watch some restoration projects and sage advice on staying alive at "Mr Carlsons lab" on Youtube
He is the re-animator!