Its not about the amount of money we will spend in treating ourselves but the effectiveness and competitiveness of medical staffs we will be entrusting our lives, right?

WRONG! the more you pay, the better you are being taken care of. Otherwise they'll just pop you full of pills and injections and send you on your merry way.
I don't know from personal experience but i have some friends that said Al Ahli (freaking expensive) is good. Also Apollo and Doha Clinics which are cheaper but more crowded