Renting doesn't build up any equity for you, but in the beginning of a mortgage you are paying mostly interest anyway. It takes half the length of a mortgage to pay off one quarter of the principal balance, if you are just paying the minimum payment.
If you rent, then you might get a landlord who doesn't fix things. On the other hand, if you buy a house, you will have to fix things yourself. Either way you end up fixing things.
Here is a handy calculator to figure out which would be cheaper, buying or renting: