If you are buying a second car, your no claims discount may only apply to your first car, but you may still get a lower car insurance quote if you have not made a claim previously and use that car insurance company for your first car.
Young drivers under twenty five could consider being placed on their parent's policy as a named driver, as insurance costs for young drivers can be high. However in most cases they will not be able to build up their own no claims bonus. Some insurers will not insure someone who is not the registered owner of the car also.
A fully comprehensive car insurance policy will cover any personal injuries to third parties including your passengers as well as your car and theirs, in the case of the accident being your fault, or no balme to either side.