Find someone who can provide well-documented examples of their good work, and who doesn’t make promises that seem too good to be true.
Find someone who inspires confidence and who doesn’t give you a quote without inspecting and testing your equipment for example. Be wary of ‘recappers’ who might lead you to believe that capacitors are the source of all evil – they are not. Whilst it’s true that older gear may need to be re-capped, many or perhaps even most faults, are not capacitor-related.
Work on classic and vintage hi-fi gear benefits from a conservative, informed approach. Changing capacitors or connectors for example might sound like good ideas, but electronic faults are nuanced and fixing something is rarely as simple as this.
Instead, I recommend looking for someone who is interested in finding the cause of a problem and resolving it, using the best parts available. This person should be willing and able to do all the little service measurements and adjustments needed to get a piece of equipment running really well. If they are able to recommend further work that will benefit the equipment, that’s great.