With the ‘log’ siding my first thought was everything black fox with orange or lime entry doors. What are you thinking?

I might go a little browner with something like SW Caraibe or Llama Wool. I'd have a warm cream (Westhighland white, perhaps) for the trim and forest green doors. Or leapfrog, if you want to go brighter.

I wouldnt be painting it. I would stain it, even if it has to be a solid color stain. Logs should be stained, not painted. I would paint it a darker cedar color. Your roof, could use a good cleaning too. Nice house, and in a nice setting. Enjoy your new lake house.

I think a deep dark green would look best.
Or possibly brown.

The paint is coming off? As in cracked and peeling paint? If so that is a good indication that the home was painted, not stained and the moisture in the wood is trying to find a way out and causing the paint to peel. It is also causing the wood to rot from the inside out because the moisture has no where to go.

https://restorelogs.com/blog/log-home-problems-with-paint/