Brains will be uploaded to machines, or human descended AI's will will be built and tasked with exploring the places it's unsafe or too time consuming for us to visit directly. The square jawed men with laser guns will have to stay at home and watch. Maybe those AI's will be built to start cloning humans once they find a good spot or something, but it's never going to make sense to ship squishy meat sacks and the metric tons of accoutrements required to keep them alive all over unless/until we find a way around the speed of light or perfect hibernation.
They might want the wood though, and they might not know how to grow it. From there we can see 2 scenarios. The likelier one hopefully being trade: we could probably teach them to grow wood, and also provide them with seeds, perhaps on exchange for some of their space-faring tech.
Alternatively there's the pessimist scenario, where they're not interested in trading for it, we're not willing to give it freely, and so war ensues.
Personally I'd just give them a few pine-cones and explain basic horticulture as a gesture of good faith, I guess the end result is rather contingent on which human they talk to.
Of course this is putting aside any ideas of deciphering our books or tapping into the internet. Not much we'd be able to do to species that can travel the stars.
Wood however... You're not gonna find a lot of wood in space.