I suggest you not to buy it in two people's name, its just a car and the paperwork for it will probably be annoying to take care of (I.e when u have to pay tax and stuff).
If you buy a brand new car, it will come with first class insurance. If you get a used one, you should ask the shop how much longer the car will be insured.
Depending on the car, it might cost you from 10k (economy) - 40k (luxury) to renew the insurance. But let me warn you, insurance in Thailand is unreliable.
My car had a small tiny scratch on the bumper and they took 2 months to approve it with so called 'first class insurance'.
It will even take longer if your car gets totalled (happened to a friend of mine).