Aaron, there is not enough info to post a great response, but here are my initial thoughts.
Always fix critical items first and cosmetic items last...anything that can cause additional damage and expenses needs to be adressed first. To me, that means the roof. You say it needs a new roof (or you can repair it for $4K)...what kind of repair, how long will it last, is there a good chance other repairs will be needed in the near future? If this is a temp fix and you are still going to need to replace the roof soon, why not go ahead and save the $4k and have the roof replaced.
From your post it looks like this is a 4-plex building. You mentioned the laundry area not having a washer...is it in the lease that the landlord will provide laundry equipment? If so, then you need to do so. If not, do you even need the laundry area? Are these coin machines that bring income?
After critical items and items that you might be contractually obligated to fix are adressed you can look at the other items, but putting things on the backburner might not be the best idea anyways, as how you treat the property and the tenants from the beginning will dictate the future of this property.
