We used SW Natural Choice on walls, and BM Cloud White on trim (a warm white) but use what you love or paint a small area and see what you think. In our house the natural choice leans very slightly green.....we used 2/3 strength in the rest of the house, except for the dining room.....we live in high desert and low humidity....which can affect how colors look! Here is 2/3 strength of natural choice with cloud white trim Here is full strength natural choice with cloud white trim.

The trim is semi gloss. For a bathroom, would the sateen finish work and still give enough contrast to the semi gloss?

Use the alabaster for everything, just use different sheen. Flat on ceiling, matte, or eggshell on walls, and satin or semi gloss on trim. Whites will clash with each other, why, take the chance.

Alabaster is a warm white, but as the other posters are saying, it's hard for us to know if that will work for you without knowing anything about the floors or your furnishings. Isn't there any way you can get access to the home for a half hour before closing so you can take over some sample boards? It is customary in our area to give buyers one short visit after inspection and before closing to be able to come over with a contractor (if they're contemplating an immediate remodel), or samples as you need to do. Ask your real estate agent if you haven't already if that would be possible. I understand wanting to have it done before you move in because it would be nice to not have the workmen underfoot, but it is very expensive to pay to have a whole house painted, especially if you end up hating it and have it all redone. If the current owners have some really horrible colors in some rooms maybe just do those couple rooms? If it's all terrible, maybe it's not a bad idea to get a clean slate. Have you used a neutral in your current home that works with your furnishings that you could use again?