A basic service is air filter, engine oil and filter once every 10k miles or 12 months. then the brake fluid should be changed every 2 years regardless of mileage.
Spark plugs can be cleaned and re-gapped for 2 services and then replaced on the 3rd.
Depending on engine type there is a toothed belt or a chain to turn the cam. It is very important that you get the belt or chain serviced before it fails as if it does you can say goodbye to over £1k for a new engine.
I think 60k miles is the sort of time to start thinking about toothed belts/chains.
Other than that the rest of the servicing is with the brake disks/pads and shoes really.
If the car has no service history I would get the engine oil and filter done along with an air filter and brake fluid change. Then I would check the brakes are not worn out, clean/gap the plugs and leave it at that. All this (apart from the toothed belt/chain) can be done yourself for under £100 and a weekend. any
help or info on doing this work yourself can be given by the guys and girls on here 24 hrs a day.