I’m guessing your model is the code 127. The rectifier is a separate component, not built-in to the transformer, and doesn’t control the voltage to the valves at all. 1% caps unnecessary. Normal 20% caps will work fine.
The variable resistors are wirewound (WW), and they can take a bit of current, but the diode is operating at a low voltage so the currents will also be low. I don’t think a tester will apply high currents anywhere, so your resistors don’t need to be high wattage. However, it is always a good idea to check the original components. Large resistors will of course require high-wattage replacements.
Read over the manual carefully and make sure you understand everything it says! 🙂