You can combine all the things you mentioned to make a quilt. For printing his team, are you talking about transferring photos to fabric? If so, you will want to research this thoroughly before deciding on a process. Some types of photo transfer are more clear/softer/better than others, and some survive washings much better than others. A 20yo is likely to give pretty rough treatment to a quilt like this, so you will want photo transfers that last.
With so many different types of fabric in the quilt, you may want to choose a batting that allows for quilting lines far apart (such as Warm and Natural). This is also the type of batting (needlepunched through scrim) that is good for tying a quilt. You may end up wanting to tie rather than quilt because of the bulk of the quilt and the variations in fabric type.
Edit: Also, what about making a t-shirt quilt? Here are links to t-shirts you could use:
http://www.walmart.com/tp/san-francisco-giants-fan-shop
Or maybe look for sheets:
http://www.amazon.com/Francisco-Gian.../dp/B0051126CS