Yay! I am totally addicted to sewing and i LOVE LOVE LOVE it! Knits are definitely more difficult, but it really is the main thing kids wear. Don't be scared though. It has a different learning curve than woven, but even on a simple sewing machine with a longer stitch length it should be fine!
If you want to start with super simple, do a simple patchwork quilt. Straightlines. Super simple.
Made-by-rae.com is coming out with a new t-shirt pattern that is SUPER SUPER simple. I got to test it. I felt so special.
If you cloth diaper, i also love her Big Butt Baby Pants (though i do find the legs are a tad wide for my taste) http://www.made-by-rae.com/2010/08/big-butt-baby-pants-sewing-pattern/
Also, Delia had great simple tutorial on baby skirts today if you are having a girl (i know you can't know... but i am still kinda secretly hoping myself) http://deliacreates.blogspot.com/2012/02/nesting-easy-baby-skirts.html
A pillowcase http://www.danamadeit.com/2008/07/tutorial-conkerr-cancer-pillowcases.html --nice straight lines make it easy
leggings (only two pieces) http://www.makeit-loveit.com/2011/09/super-simple-leggings-only-2-fabric-pieces.html-- just like pajama pants
I recommend starting small. Making something for your ds would be a great place to start and see how you like fit... then you have a model. Then trying out some patterns. When you are just starting to sew i really do recommend full fledged patterns. As you get better you can modify and change but i have a few patterns i LOVE that i just modify to make everything! (Rae's new pattern is my go to shirt pattern! I'm in love!)
I love stalking blogs and have listed the tutorial part of my favorite blogs. Don't get overwhelmed! I think it's nice to get inspiration and see if i practice that i can get better and better but if it stresses you out don't look. Just start small.
http://www.lilblueboo.com/2009/03/lettered-beanbags-wagon-cover-eclectic.html (and if you have never read little blue boo read it... she is so inspiring)
AND most of all... DON'T GIVE UP! Just go for it. When i look at the stuff i started sewing compared to what i can make now (and how long it took me) i am stunned. Keep your seam ripper close (one of my most necessary supplies...) And please post as you make stuff! Then we can celebrate the accomplishment with you!!! YAY! GOOD LUCK!