To buy a car in Dubai you need to have a residency visa.
Shop around, there are always good deals coming onto the market, especially in the current environment as there are greater numbers of expatriates leaving Dubai.
If you are considering finance for a car, talk to both your bank and the garage for the best deal.
Check out the daily newspapers, many have a very comprehensive motoring section.
Strongly consider a 4x4 as your first car, as you will be afforded more protection from erratic drivers.