In your specific situation I would suggest renting as the logical option for you. Main factor is the duration of your stay. If you end up purchasing a home and then need to sell in 2 or 3 years, you are most likely going to take a loss on the property due to insufficent time to build equity. Once you factor in closing costs, the number could be rather substantial.
Also with pitbulls, many home insurance policies will not allow them to be on the premises as they are a high liability. In that respect, it also might be hard to find a landlord willing to accept tenants with such dogs. Best of luck in your situation and if you have any other questions, please do not hesitate.