I presume that you have done all your homework and made sure that you don't need to worry about water leaking in etc..
Will you be putting insulation in the stud walls? If so, keep them out from the concrete by about an inch. It will also help with running plumbing and electrical.
Good thinking using PT on the floor.
When laying out your walls, you want to start at one end and do the layout the studs 16" OC. Since it looks like you are doing your framing in sections, keep up the 16" OC from the original wall, and don't start over. Unless the first section ended up at the length of whatever you are covering your studs with. (If drywall: 8', 10', 12' lengths)
Your next panel can end where ever it will. When you turn the corner, you can do it any number of ways, just make sure you have something to nail the drywall into. A California Corner is a way to do it.
When framing over windows in the basement, you don't need headers, but do put in something that you can screw shades into.
If you are planning on using insulation, consider using rockwool, it is fireproof, mold and mildew resistant and vermin doesn't like it as well. That is what I plan on using in my basement. Plus it is sound deadening.
I am not a pro, just an experienced DIY'er and flipper. This is just what I have learned from my years of experience and from what I have learned on here.