I've worked on a handful of silverface Fenders over the years. Definitely replace the large brown filter caps no matter what - since you weren't greeted with a constant loud buzz, they aren't toast yet, but I guarantee they will be before too long. Not even worth considering keeping them.
The black fiberboards in old Fenders are the WORST. I just hate them. They always get warped and they suck up moisture badly, which can lead to annoying noises. I've even seen them get moldy. I recommend when you replace the board for the filter caps, DON'T get "period correct" fiberboard. Try to get stiff garolite board, or even better use modern FR4 material for the board. Hoffman Amps (el34world.com) sells very nice thick board material, but you could even use FR4 perfboard. When buying new electrolytic caps, don't waste money on the Sprague Atom caps that the old timers always seem to recommend. There's nothing special about them that would magically make the amp sound better (other than being new and fresh) and it isn't what Fender used anyway. F&T caps are good upmarket choice, but Illinois/CDE is good, and the generic house brand MOD caps sold by Amplified Parts/Antique Electronics Supply are just fine - I just recapped a '69 Super Bassman with the MOD caps and it sounds exactly as it did with the old caps before they went bad.
Other things to look at: The 100K 1W carbon comp plate load resistors can be a source of annoying noise. I think Fender made an improvement by bumping up to the 1W resistors over the 1/2W ones the older amps used, but carbon comps are still notorious for going noisy when used as plate resistors. Replace them with good quality 1/2W or 1W metal film. Dale RN60/RN65 are a good choice, as are the equivalent by PRP if you want to feel fancy. They don't NEED to be 1W resistors - in fact you can maybe get away with 1/4W, that's what Peavey always used. But 1W resistors will inherently have lower noise and they also have a higher voltage rating than the lower wattage types. I do not recommend metal oxide resistors for plate loads. I've used them before on a lark and it was one of the few times where I felt the resistor type was making it sound harsh for some reason. If you want to be thorough, you should consider replacing all the plate load resistors with metal film, but it's specifically the 100K ones on the first input stages that I think contribute the most noise.
Absolutely replace the 470 Ohm screen grid resistors that are strapped across the 6L6 tube sockets. The heat from the tubes cooks them over the years and it will be only a matter of time before one fails. And again, carbon comp is a poor choice here. Replace them with larger 5W wirewound resistors. I've used Mills when I want to be fancy, but the cheapy "sand block" types are just fine. Also on those sockets are the 1.5K grid stopper resistors; good idea to go ahead and replace those with RN60 metal film while you're at it, since they get cooked and drifted off spec as well.
The Bright switches tend to go bad. Start out by giving them a good cleaning at least. You can find new replacements, but watch out that some of the newer slide switches don't line up with the old screw holes for mounting them, despite them being otherwise the same size.
Judging from the photo, this amp has one of the "bias balancing" bias controls. You'll get a better range of adjustment by rewiring the circuit to be like the older blackface style bias control. You don't need to replace the pot to do this, just a rewiring of the circuit. I believe the above linked Rob Robinette site shows how this is done. This is another thing I did to the Super Bassman, and it works as it should.
Sometimes these old silver rectifier diodes go bad. This is just a few pennies worth of 1N4007s to replace. But since you've powered it up and it seemed fine, they're probably fine.