We need photos. :-)

Yes, photos please. Your title is indicating you got a really ugly house or a really broken one, and you are trying to fix that with some paint. So telling us what is broken or you are finding ugly would be helpful too.

This photos are older but all I have at the moment - the countertops are solid surface white and stainless steel appliances. The den picture is accurate.

So what's the pig you are trying to cover?

The cabinets and continuity of color among the rooms - they go from white to tan throughout.

Slab style cabinets, IMO, are very boring & often cheap looking when painted. The variation of a wood grain gives the doors some interest. (One exception is high gloss laminate cabinet doors--a high end Euro look.)

I would add some pulls to those cabinets and leave them otherwise unchanged.

the countertops are solid surface white

The backsplash? Cabinets and counters are neutral--splash is one place you can use the blue or just about any other color you desire. Greens, aquas would work nicely with the wood.

Then yes, painting all the walls white would deal with the continuity, and if you don't like the current cabinet color then blue would probably be nice. Make sure you use samples first. That it works with the new counters and also the flooring and you like the white paint in the different spaces.

I'd do everything the same white - shoji white if you have extensively tested it in different areas in all of the rooms at different times of day. Don't do different white colors on the trim.

I concur with ci_lantro that the cabinets painted blue will look cheaper, but maybe you are ok with the more causal DIY looking vibe at a lake house. I'd look online extensively to find some slab front repainted blue cabinets to get an idea of what you are looking for. Forget any blue cabinet pics with shaker fronts.

I agree with you about the cabinets- but I really do not like them at all; and don’t have the budget to replace them. I’m hoping some simple moulding added on top and brushed gold pulls will help. Do you think the blue will make it cheap looking or just the flat front in general is a lost cause?

It sounds like you prefer a cottage look. The slab front cabinets are modern. I don't think painting them and applying molding is going to help too much. They look old - normally I would suggest replacing the doors so you can get closer to the style you like, but I don't know that they're worth it. Be careful about putting molding on top of them. Because they're a simple style you can't put standard molding on them.

I love Shoji White too, but I would use Pure White for the trim and ceiling because Shoji White is an off white, not white. Then the next time you want to repaint you have a versatile trim color that you won't have to repaint. Shoji White will look good with those cabinets if you decide not to paint them. Maybe do all the walls first and see how you feel about the cabinets. Make sure Shoji White looks good with the countertop before proceeding. If the countertop is a white-white Shoji White may look yellow next to it. Since the picture doesn't show the countertops I don't know how it's going to look.

Is this the blue paint? https://www.farrow-ball.com/us/paint/hague-blue

Have you considered replacing just the doors, then painting the cabinets?