I'd like to find some cute first underpants for a 2 yr old.

Let me start with little boys.  First there are The Small Paul Days of the Week Underwear.  These have playful Julius screenprints that decorate a colorful assortment briefs.  These are all topped with a fun logo waistband.  Made of 100% cotton, little boys will love these. There is the Pixar Toddler Boy's Cars 7-Pack Brief.  Mater and Lightning McQueen bring a smile to every little boys face.  You have a pair for each day of the week.  These have an elastic waist and fold-over fly.  These are made of 100% cotton too.

Here are some for the little girls.  Hanes Girls' Toddler Briefs are perfect for little girls.  There are 12 pairs in a package.  These are low rise styling panties made from soft cotton.  These are TAGLESS too so they aren't scratchy.  And because 2 year olds are busy, these are made for no ride ups.

Now all little girls I know are in love with the Disney Princesses.  This is the Disney Toddler Girl's Princess 7-Pack Brief.  These have all the favorite princesses on them.  One for each day of the week.  Made of 100% soft cotton. 

I hope these help you out in your search.