How can I make yarn from an old t-shirt and does the material matter?
It depends on what you're making with it.  When you're dealing with seamless T-shirts, I'd start at the bottom.  Cut the hem off, then go around and around cutting about an inch (2.5cm) in one continuous strip. You can put a little mark on your finger to indicate the measurement so you don't have to draw all those lines, and it won't need to be absolutely exact.  Don't bother with the neck and sleeves.  If you want some uniformity, you'll need to play with different widths.  You'll need narrower strips for heavier fabric.  Maybe make some test strips with the sleeves and make some samples before you start into the body of the shirts. 

The fabric is going to curl onto itself to form a strand instead of staying a flat strip if you stretch it at all.  If it's thin it will probably just do that anyway.  And that might be a good thing.