Many of the weapon properties have no effect on enhancing (I think the only ones that do are Luck, lower requirements, increasing durability, and adding elemental damage).
A lot of people are Ash-obsessed, for purposes of crafting, but there's really only a 10-stamina-point window where that extra SSI will make a difference. A few people like using Yew for the HCI & DI. A rare few, if they only do PvM, might go for oak, to get luck.
Typically, look at your target audience.
IF you're gonna craft to sell, and can't imbue, go for Ash.
If you are going to make for yourself, and can't imbue, choose your wood on your needs from Ash, Yew and Oak.
If you ARE going to Imbue the results, make out of normal wood, Imbue to the best you can, THEN enhance (as the properties that the wood adds would limit the amount you can imbue). Do note that in this case, Yew is the wood least likely to break the item in enhancing (as the other two add properties that make enhancing harder), but Yew will still be very attractive for the SSI bonus. Make your call based on what the wepon ends up with, after runic crafting + imbuing.