The help docs that ship with Adobe apps are your friends. They have detailed instructions on the keycommands you need to use to change the path tool on the fly.
1. I you create a point, hold shift, make the next point... you have a straight line, shift-click again, above or below, and you will have a perfect right angle.
2. You can also use the align tool to easily force to points to make a right angle.
3. When you make a corner point, and want to make the next point, you can just click-drag when you place the next point and it will be a curve point. OR, you can option(maybe ctrl on PCs) click an established corner point to make it a curve point in Illustrator.
Anyway, all of the relevant information can be found in the "adjusting paths" section of Illustrator CS help docs(or something comparable for Illustrator 10, 9, etc) I guess it takes practice... but I can bang out a full bezel, cpo, or side art in a few hours with illustrator. When possible, I actually use a pen & tablet to trace, and then clean up later... that makes it really fast.
As far as PSP goes, it has always looked like good app to me... I tried it last about 7 years ago, and it was a good program then. Everytime I've looked at it since, it still looks fine. If you have a copy, and it's familiar to you, use it. Don't worry about everyone else. It's often rather easy to convert one vector file to a vector file in another program, so don't sweat it.