Buying is always better you will end up paying the installment for a car that is yours and you can sell it later instead of paying the same amount for rent.
Best option in my opinion is to find a 2 years old car in decent shape. Or you can buy a new one and fix your installment as per your budget. Usually it is better to pay down payment to easy the installement.
You cannot buy a car under your name without obtaining ikama first.
If you arrive on business visit visa you can drive with international license. That case you will rent.
If you issue ikama you must do the test for the Qatari license and issue one.