For working on radios, it is good to have a multi-meter. What is really helpful is to have one where the impedance on the voltmeter is high. I have a cheap one that has an input impedance of 10 MegOhms. If you can pick one up, a signal generator is very useful. A unit that allows you to generate all the frequencies in the AM band, and the lower IF frequencies of the radios. They usually have a feature where you can turn an internal tone modulator on and off.
To start with your radio, I would replace all the capacitors and then power it up and check the voltages.
