If you close up the living room’s large opening to the hallway you create a good wall for a large TV displaying art with a floating console.

Start with some rugs that bring in the colors you love and work from there.

Move in and then take your time deciding. ie: in bedroom you mentioned adding a rug so will you be removing carpeting? Do you have furniture? A rug will have a big impact (as will lighting), so have an overall vision and build on it when adding bedding, window treatment, and accessories. Consider painting room a warm (but light shade with it being small) to create a cozy feel. Look on line for inspiration.

Follow a similar process for living room.

Maybe once you move in, show the rooms with your belongings, your color preferences, the rooms’ dimensions and you’ll get more helpful advice (in living room especially).

Bedroom:

--blackout curtains do come in white, so match the curtains to the wall as Lyn Nelson suggested. Add blackout shade in white for nighttime.

--Choose dreamy art for over the bed, neutral cover, and a throw at the end of the bed that echoes the art work.

--Choose wood night tables and small lamps as below

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Living Room:

Showing this living room to point out warm touches in a gray and white room--wood console, coffee table; ivory patterned rug; yellow throw; art work.

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--Start with art work in grays and beige to echo your sofa and chairs. society6.com has affordable art in many sizes. Look for subjects and styles you like then palettes that include gray, tan, light brown (floors).

--Consider closing up the wall opening so you have a full wall for art or flexibility in placing your TV if you plan to watch TV in that space. Choose media center, coffee table, and side tables in wood finishes like your floor to add warmth to your gray and beige upholstered furniture.

I love drapes in bedrooms so good blackout ones for sure. You need to sart by getting a bed style you love that starts the whole decor , next bedding that suits this style you have chosen , then wall color usually something from the bedding I like drapes thta match the wall color for a nice restful look. so drapes first then color match for the walls.. Satrt there then come back with those choices and we can help with the rest

Would be good to see the furniture you own instead of the furniture of previous owners so that we can work with what you have.