If going for a high-polish finish with compound, I've liked basswood or any similar smooth & tight-grained, firm wood. Balsa's OK, but I prefer something a bit firmer than that; balsa is more prone to compression, denting, cutting, gouging, etc. So it's a little more needy in terms of upkeep, with more frequent cleaning (loads up very fast) & resurfacing to be done.
For convexed blades at high polish, denim or linen over a hard backing (wood, etc) works very well with suitable polishing compounds.
Most of my stropping these days is very minimal. Little or no compound, and I prefer to maintain a more toothy bite coming straight from the stones I use. So, I've been using just bare leather (sueded side of a belt) or a piece of paper laid over an oiled stone, per HH's suggestion above.
So, a lot depends on what your objective is, as to which media for the substrate will work best for you.