I learned CAD from a class at the community college. Before I took that class, though, I took a hand drafting class. I highly recommend a class in hand drafting, because 1) the principles you learn there will make you better in whatever CAD program you go for, and 2) not every project needs to be done on the computer. Why work harder than you need to?
A drawing can only be as accurate as what goes into it, whether it's by hand or on the computer. There are some great tricks that once you know them you'll be amazed you hadn't run across them sooner. As for crisp circles and lines, it's all about the right tools. If you have a sharpie, a gel pen, a scale, a triangle, and a circle template, you can bang out a nice looking drawing. I'll dig around, I may have a sample I can upload