You could have rugs in all three spaces. Two rectangular rugs and a runner for the hall. The sitting room would definitely look more pulled together with a rug.

Bigger is almost always better. We rarely see people post room pics with rugs that are too big for the space. The rugs don't have to be identical but they do have to visually work together.

Many rug sites have tools where you can insert a potential rug into a downloaded picture of your space. This is from esale rugs.

thank you! I didn't know about a site that would do that, I'll definitely check it out!