I see a lot of SOTD straight users post stropping with linen and leather strops. As I'm new to TSR, am I doing it wrong not having a linen strop?
No. A good leather strop is plenty. Lots of folks have lots of things. It does not make them better, needed or necessary.
There is some debate regarding the value or importance of using a linen or fabric component with the leather, however I'm one who feels it is important enough to make it part of my preshave routine. It is not, as Mike stated above, as essential as giving the blade a good leather stropping. If the leather aligns the edge (much as a kitchen steel does for a chef's knife), the linen/fabric/canvas component has been claimed to...remove post-honing burrs, warm up the steel for the leather, sharpen the edge with paste, dry the blade edge post-shave. Bottom line, you'll be just fine with leather.
Leather is fine. Post shave stropping I like wool the best. I "feel" it dries the edge better. I have no proof. I will skip post shave stropping but I never skip leather pre shave.