It's fine to prime, and to paint ceilings, but sanding is a dirty, dusty job. The dust will get on your walls. The sander handle may mark walls. Stain can splash onto walls. FWIW: You can paint over stain, but not the reverse.

Take a look at SW Restrained Gold and Blonde. Those are nice honey golds without being too brassy. Glidden Water Chestnut is also nice with blue. As for the stone, it may work with a new paint color, but if not go neutral with it and let that be the accent wall. You don't want to have competing focal points. The carpet is such a striking color that you may not need an accent wall though. Perhaps just a nice large piece of art or some really dynamic fabric. I would definitely paint the woodwork and paint the adjoining dining area the same color. You can set a nice tablescape with colorful place settings for some pizzazz. And i would absolutely change the light fixture in there. There are lots of affordable options out there. I attached some fabric swatch ideas using restrained gold and blonde. Enjoy decorating your new place.

Take a look at Revere Pewter. It is a gray that depends on the light in your house. it looks very light gray in some pictures but can also go well with some Browns. My daughter used it in a bathroom with a rich brown toned vanity and it looked great, but took on a tan undertone, while still looking gray.

Thanks for the additional input everyone! Right now we have put Zinssier Gardz over the old paint (there is no peeling, it is quite thin paint actually). The Gardz is made to create a good surface for the new plaster to adhere too. I've been in and Hepa vacuumed and cleaned all the surfaces with a lead specific cleaner and removed all the plastic we had in there. We'll be covering with a new coat of plastic and tape soon and start the skim coating. The goal is to do 2-3 very thin coats using a thinned joint compound and a magic trowel. Trying to get it as smooth as possible to keep sanding to a minimum. It will just have to be a very careful and selective sanding to get ridges. The wall isn't going to be totally flat no matter what we do anyway, it's old plaster after all. I have been wondering if the kind of primer we use over the skim coat matters? Would an oil based primer be better for any reason? Another coat of the Gardz to help harden then a white primer? This definitely hasn't been fun and we'll have some hard choices going forward with the rest of the house which is all covered in wallpaper. It might just be new wallpaper for us for now. Possibly paint over it. I did that in my daughters room because her room is wallpaper over paneling so it was a temporary fix until we can drywall but it worked well. However the older parts of the house downstairs have many, many layers of wallpaper so I'm less inclined to think painting over them would work well. All of our woodwork is stained (thought the stain could very well have lead too, we haven't tested because we haven't messed with them) and luckily the windows themselves were replaced with vinyl windows so we're not dealing with painted window seals.