Welcome, welcome... you're gonna love the friendly folks here on the QB (Quilting Board).
I would just like to caution you as a newbie that I did not do a t-shirt quilt for my first project and I would recommend a simple pattern for your initiation... like Turning Twenty or similar.
I did just finish my first t-shirt quilt this past summer (and now have been quilting four years) and I did use a stabilizer so that my t-shirt blocks would behave nicely. There are several books and YouTube videos that are great tutorials. Good luck and look forward to hearing about your progress. : )