Buying Classic Audio -
Generally speaking, the bigger the amplifier, the more powerful it is likely to be and the more involved and pricey to repair if things aren't working properly. Vintage amplifiers tended to be of lower output power than modern their counterparts, so don't expect mega-watts aplenty. Having said that, 50-75 watts should be more than adequate for most domestic use, if the amplifier is of good quality and design.
Firstly and very importantly, make sure the amplifier casing is safe to handle if it's constructed of metal. Even metal cased amplifiers were often fitted with two core flex in the 70's, so ensure there is an effective earth connection somewhere. Be especially wary of designs that were intended to be housed in a console or rack.
If the amplifier was constructed in modular form with different circuits on seperate “cards”, this can lead to internal connection failures which may damage components, especially transistors. Oxidization occurs where copper contacts on the card is exposed to moisture in the air, and there is a barrier forms to providing a good electrical connection. This isn't a reflection on the quality of component, it's just a fact of life. Other than internal connectivity between circuit boards, problems can arise and with adjustable controls or "pots" as they're known. A pot can be a volume control or any other adjustable setting on the fascia of the amplifier, or it can be inside the unit setting voltage and current levels on circuit boards. These may need to be sprayed with an Isoproyl alcohol solvent to clean them.
“Exotic” components such as V-FET transistors favoured by companies like Sony or J-FET semi-conductors by companies such as Audio Note (Japan), are virtually impossible to find new, manufacturing of the particular type having ceased years ago. If these components fail you may need to source a “spares and repairs” unit. It is also worth noting that if you purchase an early Sony V-FET amplifier, it's imperative that certain diodes and resistors are replaced failing which the transistors are likely to be damaged.
British amplifiers of the 70's often utilized components that weren't of the best manufacturing quality, so it's best to budget for a good overhaul to identify failing ones. Have the transistor bias level checked too, especially if the unit seems to be running hot. The heat-sinks on which the output transistors are mounted should be warm rather then hot, after say 30 minutes of use at normal listening levels.
Japanese amplifiers of the period tended to be...well, better made overall than UK fayre, and in all honesty likely to need less maintenance if they are working nicely from the start, despite the Sony V-FET issue. Repairing a transistor amplifier is a skilled job, so it's best to have any work done professionally unless you are very confident with electronic circuitry.
Listen out for any mechanical noise or vibrations emanating from the amplifier casing. This is best done in the evening when the mains supply is at it's “dirtiest”, i.e when DC and noise is being pushed out by numerous TV's and computers into the local electricity supply. If you hear a buzz or hum from the amplifier box, the transformer inside is probably responsible. This occurs when transformer core laminations are no longer held together properly, possibly through an original manufacturing fault or separation over time. In either case the transformer will probably need to be replaced which, as you can imagine, is a difficult ask.
Buying a receiver.
A receiver is an integrated amplifier with a tuner, sometimes also referred to rather niftily as a tuner-amplifier. These units can often represent better value than the amplifier only option as receivers, especially in the UK, are currently not so highly regarded as they are in say, the US. This is despite us having some of the best FM broadcasting in the world. With the uncertainty of the future of FM in the UK, I imagine this is set to continue.
Finnally, ensure the AM antenna is still attached at the rear if the receiver is an AM/FM model. These can get broken off by careless owners who have used the plastic rod as a carry handle.
Ask for a demonstration of the amplifier or receiver before you buy. If you really, really want it because it's rare and beautiful, but on switch on it sounds distorted or is clearly not a happy bunny, turn it off immediately to avoid permanent damage. Negotiate down the price with a vegence, and get ready for a repair bill with the dreaded possibility that it will take a long time to source a replacement electronic component.