Here is 2 different designs worked up for hospital donations. Very simple double crochet with single crochet rows plus added ruffle or flower for embellishment. I personally always use Bernat Baby Sport Solid yarn when doing any baby project.
Basic Crochet Pattern: Newborn Baby Hat, use Size G hook
CH 5; slip stitch in first ch to form ring
Round 1: Ch 3, 12 dc in ring, join with sl st in top of ch 3 (ch 3 counts as first dc throughout)
Round 2: Ch 3, 2 dc in each dc around - 24 dc; join; turn on each round
Round 3: Ch 3, (dc in next dc, 2 dc in next dc) 12 times - total 36 dc
Round 4: Ch 3 (dc in next 2, 2 dc in next dc) 12 times - total 48 dc
Round 5-14: Ch 3, dc in each dc around
You can alternate colors of yarn every few rows to create a striped hat. To create a different texture you replace any row or rows in round 7-14 with sc all the way around. I did this in the pink and white hat below.
You can then add ruffle or flower for embellishment.
To add a ruffle:
Row 15: Ch3, 4 dc in each stitch around and join.