Congratulations on starting at the University of South Florida! Starting college is a lot of fun, but it also involves making a lot of decisions that can greatly impact your college experience, so it's good that you're starting your research now. When I was in undergrad, I had the chance to live both on- and off-campus, so I definitely know the importance of evaluating the options based on what works best for you specifically. USF's dorms and the apartments near USF each have their own advantages, and before you start this summer, you'll want to evaluate...
Distance from Campus. There isn't an apartment that will get you closer to the center of USF's campus than one of the dorms. However, you will likely find that your classes favor one area of campus. Review your class schedule to see where they're located. If you'll be spending most of your time closer to the edges of campus, or if you have an off-campus job or internship, it could potentially make more sense for you to explore the best apartments near USF or near your job/internship. Consider how easily you're able to get to and from campus if you're not living there, and evaluate apartments on the USF Bull Runner shuttle route. Whre will you want to be located at the end of the day so you can easily go home - or go out.
Room Layout. There are several dorm styles available to choose from on USF's campus, including apartment style, suite style, and traditional style. These all involve sharing your space to some extent, as well as sharing your bathroom. Some apartments near USF may offer a shared bathroom, though many provide each resident with their own room and bathroom. In both cases, you will likely have at least one other person living with you, unless you opt for a one-bedroom apartment. Take the time to evaluate what makes the most sense for you, based on your lifestyle. How much do you need your own space?
Cost and Amenities. Time to calculate out what you expect your costs to be over the course of your first semester. Each dorm style has a different price for the semester, inclusive of all utilities, that is dependent on the style of room. The cheapest apartments near USF start in the $500s per month, but costs build from there when you factor in the cost of utilities and the layout you prefer. You'll also want to consider how much furniture you want to invest in. Many apartments are unfurnished, while dorms provide basic furnishing, including bed, mattress, desk, desk chair and dresser.
There is a lot to consider when evaluating on-campus vs off-campus student housing, but with all these things in mind, you should be able to determine what is going to be most convenient and cost-effective for you, based on your wants and needs. There is no one right answer for everyone, but you'll find the right answer for you. Good luck, and go Bulls!