I think you would benefit greatly from some sewing classes. Check with your local quilt shop or a Jo Ann Fabric store to see what they offer.
I don't buy fabric all in the same line, because I might like something else that goes with my color scheme. Quilters use 100% cotton. Blends can be less expensive, but can be difficult to work with and don't hold up as well as 100% cotton.
As for cutting it, if you cut it on the straight of grain, it has more strength. If you cut it on the bias (on the diagonal), it can stretch easy, especially if you aren't used to working with fabric. Many pieces have to be cut on the bias depending on the shape of what you're doing (a triangle will have two straight edges and one bias edge).
Welcome to the board! There is a ton of reading here and you will pick up a lot of tips just by reading other people's comments.
There is also a Tutorial section here that you should read. That might have a lot of help for you as they usually include pictures and step by step instructions.