First off, congratulations on deciding to join the running team! That is an excellent idea, especially in college, because it helps you meet new friends and form a close knit community, gives you an outlet to turn to when school and life get stressful, and helps keep you healthy (which, take it from me, is helpful when the dining hall desserts are endless and SO GOOD).
I think the most important thing to do when you're a new runner looking for the right running shoe is to keep an open mind... even after you have bought a pair! Chances are they will not be the last pair of running shoes you buy (because running is awesome and you are definitely going to get hooked!) This is because you won't REALLY know your running style and stride (aka how you plant your feet when you run, how you carry your weight in your lower body when you run, your gate, etc) until you have been running for a while. You also might have something like fallen arches or the tendency to over or under pronate when you run, which you will not be aware of until you get started (and which you will want to invest in a good pair of shoes to help remedy). Both the Adidas and Saucony brands of shoes are terrific. However, in my opinion, I would say the Saucony would be better if you intend to only wear these shoes when running. Still, since you are new and do not really know what kind of shoe you truly need, definitely do not overspend on your shoes. Investing a ton of money into the wrong shoe would be silly, so try not to spend more than $100 (even closer to $80 would be wise if you can find it).
And definitely go to a running shoe store. The sales attendants at these stores are extremely helpful in helping find the perfect shoe for YOUR feet. (Again, keep an open mind! They might suggest an entirely new-to-you shoe that you didn't know about beforehand. But it can't help to just try it on, walk/run around the store, and see how they feel on your feet.) A lot of times, these specialty stores will even have the technology to examine your feet and your running stride, and match you up with the perfect shoe.