If your goal is to go to PT school, do not bother going to a private institution or worrying about the prestige of your undergraduate college. It does NOT matter in your application.
What does matter is a strong GPA, a strong GRE, strong references, a variety of experiences working or volunteering in clinics, extracurricular activities, and your personal statement. I went to a state school, and I got into 7 of the 10 programs I applied to (two of which were in the top 30 programs in the country). I also got into the three schools I liked the most from my tours and interviews.
Considering how much money DPT school will cost, you are going to want to have the cheapest education possible for your undergrad. (Think about paying off student loans that are equivalent to buying a house if you combine undergrad and grad school debt).
Lastly, in regards to major, I STRONGLY recommend you study something that stands out but still helps you get the necessary prerequisite courses. It is a lot harder to stand out to a program as a biology, a kinesiology, an anatomy, or an exercise science major because that's what so many people study before PT school. These aren't bad degrees, but it is a lot harder to stand out when there is 20 people with this same degree with similar stats competing for the same spot. It's not impossible, it's just harder.
I studied engineering in my undergrad, and it was the NUMBER ONE thing I was asked about during my interviews. Interviewers were always so interested to hear me talk about it because it was unique. I'm not saying you have to study engineering to stand out in the application process, but I am giving you an example. Look into the degrees offered at your school, and see if there is one you are interested in that you think will make you successful (and provide you a back-up plan). Heck, you could double major or something. If you do decide to study one of the degrees that provides a more traditional route to PT school, find other ways to stand out in your application.
Your undergraduate education will be what you make of it. Challenge yourself, keep your grades as much as possible, be involved in extracurricular activities, look into doing research, etc. Doing these things will prepare you well for DPT school - not the prestige of the school. I hope this helps and good luck with everything.