There is a couple of options available, the public transport system in Cape Town is not to bad especially not the MyCity bus service (I would however avoid the metro train as it is quite dangerous), then there is buying a car cash, you will be able to get something very decent, reliable and save for about R50K. then in terms of long term car rentals there is a few options that include Avis and Tempest. I have personally used a new car rental company called pace car rental and I was blown away by the quality and level of their service, their main office is in Johannesburg, but they have presence in Cape Town.
Good luck with your move and I hope that you get your transport issue sorted.