Should I follow a crooked wall or try to plumb the new extension?

I've dealt with this same scenario on renovations where nothing was square. Tapering the lean over the length of the wall is the move here. If you carry that 3/4-inch lean trough the entire 25-foot run, you're going to hate yourself when it's time to install baseboards or if you ever decide to put a door at the far end. A door on a wall that's out of plumb that much will never stay where you put it; it'll just ghost-swing open or shut constantly.

Start your first stud flush with the existing wall, matching its lean exactly. Then, over the next four or five studs, slowly bring it back to plumb. You’ve got 25 feet to work with, wich is plenty of distance to hide a 3/4-inch correction. If you spread that adjustment out, the transition in the drywall will be so subtle that no one will ever see it, and you won't be fighting a massive hump of joint compound.

For the ceiling cracks, I'd recommed cutting back the old drywall about 6 inches to expose the existing framing. This lets you tie in the new top plate properly and gives you room to install some **solid blocking** between the joists if they're running parallel. It makes the tape joint much stronger and less likely to crack again when the house breathes.

And definately use a long level or a laser to check your progress as you taper. You want the transition to be a smooth plane, not a series of zig-zags. Once you hit plumb about eight feet in, just run the rest of the wall straight. It’ll look proffesional and save you a massive headache during the finishing stage.

If the old wall is leaning 3/4 of an inch, does that mean the bottom of the new wall starts in a diffrent spot than the top? I'm trying to figure out if I shoud just snap a chalk line for the bottom plate and ignore the lean until I start framing the studs. I'm also curious if I should use shims on the studs to get that taper, or if I should just move the top of each stud a tiny bit over on the plate to close the gap? I want to make sure the drywall acutally sits flat when I get to that part.

Snap that chalk line on the floor first and keep it dead straight for the full 25 feet. If your bottom plate isn't a straight shot, the whole room will feel off. As for the taper, don't mess with shims on every stud—that’s a recipe for wavy drywall. Just shift the top plate. Start it flush with the old leaning wall, then over the first 8 feet or so, gradually angle the top plate back til it's perfectly plumb with your floor line. Once the plates are set, your studs will naturally follow the transition. It’s much cleaner than trying to eye-ball each individual vertical.