I also need a rug but I'm not sure how big I should get.

Is the coat closet frequently used, or just when you have guests? I would recommend a shoe storage bench that can be moved, should you need to access the closet, but you wouldn't want to do that every day. If you are set on a built-in, you could always switch out the door to a folding one, so it doesn't open up as far.

What do you use the coat cupboard for, if not coats, then maybe smaller stuff..?
-you could remove coat cupboard door
-build storage bench from inside cupboard to front door (having storage inside bench lid)
-upper part of old coat cupboard could have sliding metal mesh pull-out drawers and then add a shorter cupboard door above bench height. So basically you loose the bottom of the coat cupboard but still can use top 2/3 as a storage cupboard.
-run a runner so kids in wet boots can walk to bench. Nice friendly colour mix on rug (orange,red,yellow, etc).

This is a radical idea...You could use the bookcase for shoe storage. Move it so that one end is perpendicular to the wall between the window and the door. Have the shelves facing the door so you can put shoes in it. Use the top for a plant - large decorative dish or basket for keys / mail, etc. This would also serve to create an "entry" area separate from the living room.

it really depends on your budget, i would suggest bay windows with window seats.

or you could attempt to make it into a little room by adding a wall of floor to ceiling bookshelves