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.danamadeit.com/tutorials
http://www.makeit-loveit.com/tutorials
http://www.made-by-rae.com/tutorials/
http://homemadebyjill.blogspot.com/p/tutorials.html
http://www.craftaholicsanonymous.net/tutorials
http://www.craftinessisnotoptional.com/p/tutorials_06.html
http://www.iammommahearmeroar.net/p/tutorials.html
http://deliacreates.blogspot.com/p/tutorials_28.html
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!
Any questions?