My first sewing-for-baby project was this nightgown from an old tshirt. I used the pattern from this website.
Took me longer to put together the pattern pieces than to actually see the gown, and so I planned on making a few more, but never did. Baby E wore this one time; it was a little short for her. I'll definitely keep this pattern in mind for gift sewing.
Next up in sewing-for-baby: flannel blankets. Used the tutorial found here and flannel from Joanns. These were super easy, and we've been using them all the time. The flannel is nicely absorbant of baby drool--these are great for tummy time. If you can buy the flannel during a sale, these could be a very inexpensive but useful gift.
Newborn baby pants were next up. Used this pattern and Hawaiian print fabric leftover from when I made pj pants for the family 3 years ago. Baby E never actually wore any of these! I made one more pair out of an old shirt that she wore once, but I dress her mostly in one-piece footie outfits (so much easier). These were fun to make, and turned out cute, but just not useful for us.