If it were long term, I'd just let it dry out and stick it wherever. Then, before you do your set up, take it out, shake out the spiders, and soak it for a few days or so before using it.
If it's relatively short term, I'd just keep soaking it. As to the algae, if it's small enough, you could boil the piece of wood, otherwise adding some bleach to one of the soaks should take care of the algae.
Even just keeping it out of light might work, and if you have snails in any of your tanks, maybe toss one or two in, they'll likely clean up the algae for you.