I built a steel stand for mine. One, it gives me storage underneath, and two, it's easy to slip a hand truck under the legs (as I designed it to) to move it around.
The only benefit to wood is that it tends to help dampen some of the "ring" of a good anvil. Your HF anvil is cast iron, so that's not an issue. (It wouldn't ring if you threw it at a church bell.)
Wood is "traditional" simply because stumps and sections of log were easier and cheaper than any alternative in years past. Before 1900, premade structural steel was ghastly expensive, masonry wasn't much cheaper, and that just left wood.
Conversely, today the opposite is true. Anyone cutting a fair-sized Oak down- or any other good hardwood- likely isn't going to give it away. The wood is valuable, and some areas even have people going around after storms buying downed trees.
Lumber from the hardware stores is dirt cheap, however, and it's fairly easy and reasonably inexpensive to bolt several sections of 4x4 or 6x6 together with lengths of allthread.
But really, anything will do. I've seen anvils mounted to mortared pillars of rock, stacks of loose (as in, non-mortared) bricks or cinderblocks, even sat on old chairs. Whatever works for you.
Doc.