I would start now. Even if you just cover the area with something light-excluding like tarpaulin/black plastic/mypex it will deprive the weeds of light in their peak growing season and they will start to die. Personally, I like to put a small amount of compost underneath at the same time to give it all a kick start, but it’s not necessary.
When you start to build your beds in earnest depends on the state/age of your compost and your available time. If you have well-rotted weed-free compost you can leave it all until just before you want to plant. If it’s less well-rotted/lumpy you might benefit from spreading before winter so the frosts can break up surface lumps and produce a fine tilth. It would be in situ then for hoeing off your spring flush of weeds before planting.
Up to you. Timing’s not critical. Just don’t plant into fresh (hot) compost, and check first whether you are using anything that could contain aminopyralid weed killer. (Lots of info on this site)
Good luck. Must be lovely to have a ready source of manure. Enjoy!
Jan
