The quality of a gearbox depends highly on the previous owner(s). This means that you can find out what the general condition of a car is by just checking the gearbox. A poorly functioning gearbox can very well mean that the car in general has been treated badly. An important part which you should check in combination with the gearbox is the clutch.
Have you found a car that ticks all the boxes, then you should try to get a discount on the asking price. Because there is always a margin of profit, between the asking price and the dealers purchase price, it is up to you to negotiate the best possible deal.
The tyres of a car are in plain view and therefore easy to check. In order to find out if the tyres are still in good shape, you need to check each tyre individually. Start by measuring the depth of the tread, this will give you good idea of the lifespan. Because a tyre needs a minimum of 1/16th of an inch (or 1.6 mm) tread depth for MOT approval.
When you are buying a car from a private person, it is sensible to put a couple of things on paper. A purchase contract, like you are used to from a dealer, is not available. To still be able to draw up a contract, as a seller or buyer of a pre-owned car, we have made one for you, that you can download here.
