This space is actually something we're planning to tackle right away, which I'm sure comes as no surprise (wait until you see the rest, though, and you'll understand why we wrestled with keeping it as is to do something else first instead!).
The doors inside will go, and we'll have a beam put up to secure the structure of the house (since that used to be the end of house, it needs some special support). The crazy windows will be replaced with two sets of double windows in the front, and then the hardwood that's hiding under the living room carpet will be carried throughout here. Down the line, I would love to think about moving the entry way to front of the house (it's currently on the side), and maybe adding a closet where that window is next to the real front door. And maybe a wall? We'll see how things progress.
The bigger issue is something you can kind of see here - the wall on the other side of that door is actually covering up a fireplace. It hasn't worked for ages (maybe ever?), and square footage is at a premium, so we're going to have it removed so we can open up that wall, which goes into the dining room (and it also cuts into space in the upstairs bedrooms, which is a bigger problem)
Because of these issues (and a few others with the basement and roof, eww, worst places to have to spend reno dollars), we're going to keep our apartment for the month of August and move in about a month after closing. This will be a totally magical renovation where the things I mentioned will all be completed before we move in! (Absolutely not true, but I keep telling that to myself anyways!!!)