OP here. Thanks for the advice!

I wouldn't go smaller than an 8x10 in a large room like a living room. 11x14 is best, but I realize they're costly.

Smaller rugs are meant for hallways or entry ways.

The general rule of thumb is that a rug looks better when it's not "floating." So, it should be anchored by at least part of the couch.

We currently have a an 8x10 rug under our sectional sofa (placed in the corner of a room). Do you think downsizing on our new rug would be a bad choice? Should the edge of the rug go under the sofa or is it ok to have it an inch or two away from the sofa?