I decided to start in the back, right corner of the basement and work my way around clockwise. This way I'll get some "wall building" practice before I build the most prominent wall- a 28 footer that stretches the length of the room.
The downside of this approach is that I had quite a few obstacles- pipes and main duct to deal with right off the bat. Since the first section of the wall has lots of copper pipes to work around, I thought about nailing the top and bottom plates, and then toe nailing the studs (see method 2 of How to frame a wall).
In the end, I decided to build it on the floor, cut out the necessary parts of the top plate, then tip it up and nail it into place. I bought a compound miter saw, a jigsaw, and my 1st load of lumber over the weekend.
Basement remodeling tools
For the miter saw, I went with a DeWalt 10" because that's the brand I've seen a lot of the pros use. Also, it was comparable in price ($197) to most of the other quality brands. The jigsaw is a Skil 5.0 Amp Orbital Jigsaw. I went with it over the DeWalt because it was half as much as the cheapest DeWalt. Hopefully, it will work out OK. I spent over $400 on my two trips to Lowe's.
Lumber tip: Many people just 'eyeball' the 2x4s they're purchasing to see if they're straight. A good way to make sure is to place each one on the floor and roll it to all four sides. It takes a little time, but you're sure to end up with straighter boards which will make framing much easier! A little bow on the long side of the board is OK, but avoid the ones that are twisted or bowed on the short end.