I really like natural fibers when possible, so I tend to use Blue Sky organic cotton. It’s a very soft cotton that washes up well. I also really like Dale of Norway’s Baby Ull. The Baby Ull is a machine washable merino (soft) wool and comes in a wide variety of colors.
There are some lovely free baby and children’s clothing patterns at http://www.garnstudio.com/lang/en/kategori_oversikt.php
Jean Greenhowe has some lovely toy patterns, and bluesky has the popular Baby Bobbi Bear pattern http://www.blueskyalpacas.com/pattern_detail.php?patterns_ID=2
Cotton doesn’t have much stretch, so some people find it hard on the hands.
I love knitting for little ones!
Edited to say that I re-read your post. The patterns above may be something you bookmark. They aren’t really beginner patterns, but I’m sure you will be ready to move on to them in no time with all the helpful people here.