TLDR: Moved into an apartment where the drywall/walls/paint have been horrendously maintained. Want to redo the walls- advice?

So my guy and I just got the keys to a new place today (yesterday at this point), and we're psyched! It's a great little apartment, great location, great price, and, best of all, not in my Mom's basement. However, as soon as we became the keyholders, we realized how terribly it's been maintained.

We want to make it work, and are both hopeful about the situation. We cleaned a lot tonight- and were prepared to caulk things and fill in holes and were planning to prime things for painting afterwards, but the drywall jobs in the place are consistenly awful. Awful enough that I can't justify applying the expensive KILZ primer we have to them... Beyond that, most of the windowsills are gummed up with gobs of latex paint, and there are large paint drips all over the place. Seriously looks like the person drywalling and painting gave less than zero fucks, and smoked 2 packs a day... there are nails buried in the paint, staples are all over the place... You get it, it's a fixer-upper to say the least.

We're still in my Mom's basement, in the same town as the new place, so we've decided to stay a little longer while we correct the terrible walls, at least (if anyone has any tips on the awful window paint issue I'd love to hear them). Our plan is to buy a palm hand sander, smooth what we can, and then use mud to fashion a smooth wall over the terrible ones... I'm wondering if this is a good plan? Anyone got any advice?