Here are pics

Are you going to put a run down and how much is the budget?

If you are going to put a rug down I'd figure out the rug and then decide about the floors, if the rug covers it I probably wouldn't go through the hassle of refinishing. I actually really like the stained wood trim. This stained wood is of far better quality than the white mdf you get most of the time now. If it were me I would refinish the base boards as needed, paint the walls, and then add a nice stained crown molding to the space to match the baseboards and built in.

And a new light fixture.

As for the window, what type of window is it, does it have a storm? Where are you located? In some parts of the country you don't get much of an energy efficiency advantage from a duel paned window vs a single pane with a storm so if it's an old wood window it might be worth keeping, it's just a matter of preference. Call a window contractor.

If it's a wood window with an aluminum tract it's probably not worth saving and if it's an aluminum window I would definitely consider replacing. Replace with an appropriate style to your house, probably wood. A little more expensive than a vinyl replacement window, but it will look better and last longer.

It looks like it is time to have the floors refinished. The discolouration may or may not remain once the floors are sanded. There have been some great restorations of stained floors on houzz. Apparently a little bit of medium stain can be applied to the floors to help camouflage the colour differences. Not only are the floors stained to a "fashionable" colour palette, the stain hides any discolouration. Kind of a win-win situation.

The cost of refinishing the floors should be (roughly) the same price as a medium end engineered floor or HIGH end laminate. The quality of your flooring will be much higher if you keep the old floor and have it refinished.

If you are going to have the windows replaced...I suggest you get them done FIRST. There is nothing more heart breaking that having your beautifully finished floors ruined because of construction dust/water stains during a renovation.

I live in Lakewood, OH. Next to Cleveland. So it gets quite cold. We were told by the inspect to get new windows when we can. They are all wood. The outside of our house is yellow with white trim. The previous owners have already painted some of the interior trim white.
We are going to get a new light fixture.