I'd have to agree with rudestuff's basic assessment.
Absolutely, finish the university degree. As mentioned, most US airlines require a college degree, and, it's always a good plan to have some education/skills outside of aviation in case things don't work out, furloughs, layoffs, etc. Yes, right now, there's a pilot shortage, but, just wait, that'll change. Or, as a pro pilot, you're always just one bad medical issue away from not being able to fly.
In the US/FAA realm anyway, the typical path for pilots is usually PPL, then Instrument Rating, CPL, then CFI. As an instructor, that's where most folks build their time towards professional flying. It's a goofy system, as the youngest, newest pilots are the instructors, but that's the way the rules are written, instructing is one of the first things you can do to get paid (though maybe not very much) for flying. At least someone else is paying for the airplane time. By the way, you may already know, but Part 135 such as Ameriflight, by regulation, require 1200 hours minimum for PIC's. For a VFR-only 135 pilot, it's 500 hours, but realistically, there aren't very many VFR-only 135 jobs.
So, what to work on while finishing school? IR would be the next logical step. However, it's a lot of knowledge-study, as well as the flight training, that may be hard to devote proper focus towards while taking university classes. Everyone's different, but I just recall finishing my degree, with a full load of serious courses, I barely had time to crap (it all worked out, couldn't afford much food, either!), let alone delve into intense extra-curricular activities. IR is perhaps best accomplished with a minimum of two lessons a week, more, 3 or 4 a week, is even better, for most efficient and cost effective training. Not saying it can't be done otherwise, just a suggestion to realistically consider your personal situation and capabilities.
Owning your own plane for training can be a great way to reduce costs, but, that has the potential to cost more than renting, as well, if, say, some unforeseen large expenses crop up, maybe an engine failure, or other major repairs. Not that likely with a basic airplane (152, 172, whatever), but, things happen. As rudestuff put it, "Super cheap if nothing goes wrong.."
What to do, then, while finishing uni-? Instrument rating, yes, if you can spare the time/energy/brain width, etc. One option, actually, might be, to work towards the commercial certificate first, while in school, the studying and flight training, are, perhaps less intense than IR. A CPL without instrument rating is very limited, 50nm radius, daytime only, not very practical except for, maybe, cropdusters. But, that limitation is removed once your IR is obtained. Whether you own a plane, or not, you can certainly point towards logging the basic required experience (cross country solo, night hours, total time, etc.) listed in Part 61 for both IR and CPL, whenever you get to go fly.
Lots of choices, you pick what might work best for you. If you have a local favorite flight school/instructor, sit down with them and discuss possible plans in detail.
Good luck, have fun!
(Disclaimer, internet advice only, worth exactly what you paid for it!)