Just be careful of the faceplate cleaning, some of the old vintage stuff becomes easy to dislodge due to age, even with water. Clean, dry and possibly clear coat it to protect the decals.
The speaker will be interesting - I can't see it but given the age, it may be used as a choke with a electro magnet rather than a ceramic/alnico. There are paper rebuilding/reconing speaker specialists, not cheap but will do the job if that's terminal.
Lastly check for wood bugs.. older amps get left in rooms and other locations out of the way.. the same places woodworm etc likes.
Question is - do you want an old looking amp with rejuvenated innards or a cleaner restored outer with a clean front mesh?
If it was me, I'd quickly check the power and output transformers (out of circuit), I'd strip it down, treat the corrosion on the chassis (assuming there's no manufacturing stamps etc). Test each component, and make the chassis and speaker both safe and functional. There's a risk doing the outside beyond a simple dust.. when you start cleaning you can rinse out dyes, warp wood, and it will not be back to 'new' anyway... so I'd probably do that - dust/vacuum it, stablise any rips/tears and carefully clean up the face place if it can take it.. The switch gear/lamp/pots can be changed and still have the same look and feel so that's not a biggie to resolve. On the speaker - you want to check this first, if you're going to restore it.. then sending it away and getting it back takes time.
All in all, there's nothing that should stop you from having an operational piece of history. I had a rock salt needle stylus on my receiver - they degrade over time and so do the spares whilst on the shelves, the result is there's no replacement possible, the rest works really well (at least until they retire AM/FM), the magic eye works still, and at the moment the EZ80 is sat in my guitar amp
