You could use suede, I suppose, but I've found that the smooth side of 2 to 10 ounce leather works well. Heat it up with a lamp, hair dryer, heat gun, or whatever before rubbing in green chromium oxide (or your choice of colors and grits).
My strop is leather, smooth side up, mounted on a (approx.) 3" x 11" piece of 5/8" mahogany. Mahogany is stable and I have lots of it - you could use whatever you have at hand.
I buy leather at Tandy, but not online. As far as I can find, you have to buy a side from them - I go to their walk-in store in Albuquerque when I'm up there. You can get 12" x 12" pieces of vegetable tanned shoulder, from 6 to 9 ounce, from knife suppliers. Do a search for Jantz, Texas Knife Supply, etc.
You're hankering to get to work stropping your blades now with locally purchased stuff, I know, but you'll only need to wait a week or so if you order your parts online (at least, the parts you can't get locally). As far as the green chromium oxide, I bought mine at Woodcraft - a 6 ounce bar for $7.00. I have some white that another forum member sent me, but I don;t use it much. It's Thiers-Issard, some French or other European gunk that goes on the leather pretty smooth. He sent to me a Spyderco Delica that he stropped with that white stuff and it was the sharpest knife I ever held.
Here's a photo or three of the strop setup (and convex sharpening pads) and some rouge....
The strop you see is green chromium oxide on smooth leather. The other side of that board is rough leather.
Formax chromium oxide $6.95
Formax and white Thiers-Issard