The logs are real twigs. I bought a packet of fallen trees/deadwood from HobbyCraft as these twigs tend to look a lot more like small scale logs and branches rather than just twigs, for e.g. the big one on the base w/ the dead Hunter Orc.
I didn't paint the, separately, I painted it all together. If you'll notice, most of the spiders are quite far off the ground which allows for the paintbrush to easy get to the spider's underbelly and the base easily.
If you weren't sure that you'd be able to do it carefully however (a position I myself had been in for years), then I'd recommend doing it separately. Make sure you try out where it all fits on the base before painting if you do this option. The last thing you want is for your beautifully painted spider to not fit on it's beautifully arranged base.
Good luck