I use 3/8ths inch Sure-Ply or Ultra-Ply underlayment. Extremely strong, and best of all, very very stable. You can typically get Sure-Ply at Lowes or Home Depot. Ultra-Ply is absolutely the strongest, but you may have to order it at the big box store.
But be forewarned, this stuff ain't cheap. And, you can only buy it in 4x8 sheets.
As for a template, I just bought a piece of white poster board at Dollar General for 50 cents, laid it underneath a one-quarter circle of the track, measured an marked a point one inch outside of each rail in the section, then just connected the points freehand with a pencil to create the curves on each side. Then I cut out the curved paper section, laid it out on the underlay, and traced the paper edges onto the underlay. Then, I very carefully cut out the piece of underlay, so that I had a nice neat quarter of a circle.
Then, I used this piece of underlay as a template to mark the underlay for every section of curve that I needed. I never cut or altered that template piece.
You wont be able to cut the underlay with a razor knife. You are going to need a small hand-held jigsaw with a very fine blade, and take your time.
Hope this helps.