I would like to start a small company that produces custom t-shirts for universities (like t-shirts in most of the North America's university bookstores).
I already have design with a couple of university logos.
Now, I am asking for directions to consider before starting this thing, e.g.:
While there might be an exception to this, all of the universities that I am aware of in the US have trademarked their logos and name. This mean that you must license the use of each university's trademark.
Fortunately (depending on how you think), many universities have a single third party handle their trademark - The Collegiate Licensing Company. This third party also has a variety of requirements that you must meet before they allow you to use the mark.
Before you determine your price points, you need to know your costs and licensing, along with the requirements imposed by the licensing company, will be a big portion of your costs.
As for the legal issues, I would talk with the universities, since they do own the trademark to their name, and in any case you don't want a legal battle with them (you will loose on public opinion alone).
I would suggest reading "the four hour workweek", since there is a theoretical example in the book of how to sell t-shirts, and an explanation of best practices for that.
One of the things you can do for example is buy a relevant domain name (about $9 a year) and build a landing page that explains your great t-shirts, with a "sign up for more info". After that, you can buy some Google ad words to test and see how many people click your link and sign up for more info. If the numbers make sense, great, you can start your business. If not, you can test other key words and ad copy to see if you can improve things.
As for pricing (once you decide to start the business), I would suggest testing different pricing models to see what works best. Start with the price that your competitors have as a baseline, and see if you can charge more or less then them.
If you don't want to deal with inventory risks, you can also start your business with CafePress or Zazzle, which will leave you with smaller margins, but no real risk.
I suggest you look at t-shirtforums for more information.
Here's a good blogpost on the challenges of trying to make money from T-Shirts. Perhaps note entirely applicable to this situation, but plenty of good advice nonetheless.