Great question! I think the answer depends on how strong of a student you are, and how well you adapt to change.
If new environments, new people, and new routines are no problem, then you can probably head straight to the university with little difficulty. Of course, part of that equation depends on how large your destination university is, what classes you will be taking, and how many classes you will have each semester.
I graduated from high school well within the top 10% of my class and started classes at The University of Texas in Austin that Fall. Even though the expanse of the university and number of students (one of my history classes was bigger than my entire Senior class) took some getting used to, overall the transition was fairly painless.
I'm glad that I went directly to UT. I also took some classes during the summer at UT Arlington, and the differences were pretty astonishing. UTA felt a lot more like High School, Part 2 to me than attending class at UT. For some, that would have made for a better transition after high school. For me, I preferred getting thrown right into the mix at a major university. When I returned to Austin for my sophomore year, I felt much more at ease with making my way around campus and with handling my class assignments.
Ultimately, it will be up to you to decide how much of a transition you want or need. You can always pick up core classes at a community college during the summer (much more affordably than at your university) while attending major-specific classes at your chosen university.
Good luck with whatever path you choose to follow. I hope you have a great experience either way!