I came from the same type of family -- no traditions -- no heirlooms. So, needless to say, I have started many of my own for my kids. 2 that you could EASILY do would be yearly Christmas ornaments and keep shirts, blankets, etc from important events (first picture, christening/baptism, first day of school shirt, favorite shorts etc.) and collect those to make an heirloom quilt of their childhood. Then, when you know who they are as adults, you can build the color scheme of the filler quilt pieces to meet their own needs.
Good luck!