We had a sump pump in the basement, well we still do, but it isn't noticable anymore. They can be really unslightly, but you can avoid making them a fixture of your space.
Our solution was to give it its own room. We banged together a wall around it and put a door on it.
You would still want to frame it to code, which is usually 16 inches between studs in our area. In some areas, it can be down to 12 inches, or up to 24 inches depending on the load being supported. As yours would not be load bearing, I would just check code to see what the options are and calculate out the minimum amount of space needed to cover the area as I am guessing you don't want it to be a focal point.
I would run it up to the ceiling to avoid creating a shelf and another spot for dust/spiders/crap to gather and just consider the space a write-off. If you do that, you might as well put a regular door on it.
You can get prehung doors that are 18x80 if you are looking to minimize the doorway.
Of course, you could always build a short shelf over it and put a cabinet door over it, but you might want a little more space should you ever need to get in there later.
Just make sure it's done to code.
As for a door something that I'd personally suggest a simple closet style track door. Nice and easy, looks clean, and it's basically going to be a closet.