It depends on what you want. At the very beginning I didn't sew the liner either. The thing with not sewing the liner and pulling the lining tight enough so that it's unlikely to move is that the material can come together in the center and create a tight spot like a funnel. Also it's necessary to fold the material to keep it from fraying and this causes a bulge inside the tube that adds extra pressure to the finish. Sewing is much better, stronger, and easier to deal with when lining the tubes. As for how wide to make it - I make it so that the resulting liner has a slightly larger diameter than the tube it's going in to account for the stretch.
The material I use is a cotton/synthetic blend that doesn't absorb moisture. It's very soft to the touch and strong. If you use something like felt then it will pill (shed) easily and will retain moisture. You want to find a fabric that has very little friction. You would be surprised how "grippy" some fabrics are even if they seem to be sleek.
For me a fabric that I accept for the liner has to pass these tests.
It must be non-abrasive and soft to the touch.
It must not retain moisture.
It must be strong.
It must not be too stretchy.
It must allow the cue to slide easily with all sorts of wraps.
It cannot be to thick to use in the tubes - this comes into play mostly for the small tube.
There aren't a lot of fabrics that fulfill these six criteria that I have found.
