While a visual inspection of the inside of the amp is helpful, one sort of needs experience to spot a burnt resistor or a bulging capacitor or other visual signs of distress. Having access to a tube tester is also nice, but decent ones are not cheap.
I don't think testing capacitors makes much sense. Capacitors generally can be tested only if they are removed from the circuit. The only in-circuit test that might indicate a problem is ESR (equivalent series resistance), and this is at best a rough measure. Also, most capacitor testing that can be found on multimeters is essentially useless because they only make measurements at very low voltages. The proper meters are dedicated capacitor/inductor meters and these can be very expensive (common price for a used high voltage capacitor tester is in the $800 plus range).
It is best if you can find a dealer or someone in your area with experience with tube gear to check your amp out. At 10 years of age, your amp is pretty young. My tube amp is about 15 years old, but, it is built mostly with parts that are in the 70-year age range (only the power transformer is "new"). I have not had to so much as replace a tube during this time.