How old is the car? I work for a franchised dealership and if we sell an extended warranty whilst the car is still in its manufacturer’s warranty, then the extension is just that, an extension with no loss of cover (except the radio system, strangely).
However, some 3rd party warranties have claim limits, either a maximum per claim or in total. Best start by asking for a policy booklet before deciding which one to go for. Be aware that as a car gets more and more miles on it, then a number of things will not be covered due to ‘wear and tear’. Also, most aftermarket warranties will not pa for diagnostic work to be done. So if you have a fault and it is not clear what it is, a garage may ask you to pay the labour of finding the fault before they approach the warranty company to pay for the repair.
As a rule, you’ll get what you pay for, a cheap warranty won’t cover much but a dearer one is more likely to give you better cover. Search for ‘mechanical breakdown insurance’ and see what you can find.