I also recommend getting a brother. Under the $150 price point, stay away from Singer! I've had a lot of experience with low-end Singers through teaching sewing and by far I've never had the problems with my $80 Brother that I've had to deal with low-end Singers. I also recommend a drop in bobbin instead of a vertical loading bobbin. You should also think about getting a machine with a one-step buttonhole if you are going to be doing a lot of projects with buttonholes.
I agree that old sewing books are an excellent wealth of information. However, you don't really NEED to have a book, most of these things can be found on the internet.
I have a pinterest board for sewing technique tutorials that I found useful - http://pinterest.com/jordannhall/sewing-techniques/
Also See Kate Sew has a lot of excellent beginners info that will help you out http://seekatesew.blogspot.com/p/supplies-i.html
In addition to ALL of the things that marypoppins mentioned, I also recommend:
- A loop turner, I use mine pretty frequently. http://www.amazon.com/Prym-Dritz-R-Loop-Turner/dp/B000Y3GS5E
- Pinking shears would probably be a good idea
As for starting sewing patterns. Simplicity has a line of "Learn to Sew" patterns. The main difference with these patterns is that they include a lot of extra info in the instructions. Simplicity's "Perfect Fit" line has a lot of useful information on fitting your garments. A solid beginning project is always PJ pants.
As for your cat, my old man does what he wants ,where ever he wants, whenever he wants. He's also a large (not fat, just large structured) cat with long grey fur... fur that gets everywhere. So, it's not about keeping your cat out of your projects it's about keeping your projects out of your cat's way. Store your fabric in places that your cat can't get to in order to sleep on top of them. Don't leave fabric/pattern pieces laying around for long periods of time if your cat is going to mess with things. My cat loves to play in the pattern tissue paper, so watch out for that.