Christian, if I were planning my first safari and had some budget constraints - then I would go to South Africa for 6 days.
I would spend the first three days hunting some of the more common plains game where you are most likely to enjoy some success - species such as blesbok, impala, springbok and wildebeest.
Then I would dedicate the second three days to hunting some of the naturally occurring species, so that you get a taste of hunting wild Africa. So species such as bushbuck, reedbuck and bushpig would be my pick.
If you have more time and money, stay longer! If you want a "real" plains game hunt then maybe go after sable in Zimbabwe and stay on to chase a few more antelope. Truly wild and free animals are earned and you'll treasure the experience.