I have the Kohler Caxton sink K2210. The interior dimensions are 12x15. I believe it is 7 inches deep. I find this sink to be plenty big enough for bathroom use. The oval shape also gives you a little more countertop area than a rectangle shape. You should be able to get it in white for under$100. Home Depot has them on their website at $67 dollars.
Here's how they look installed in my 60x21 inch vanity

Plenty of room behind the sink, especially if you don't have an estcheon plate like I do because of a miscommunication by the plumber to the fabricator regarding faucet hole.

Thank you for the visuals badgergal, that was very helpful and nice to look at! The kohler looks as though it would be easier for me to keep clean as it all dips to the drain. While I love the look of the rectangular Nantucket there is that bit on the bottom that looks sort of flat. Of course husband likes that one because he does not clean the bathroom.

I have ordered the 12 x 12 square under mount for our 24 inch vanity. Would love to get feedback as this is my first bathroom remodel. http://www.americanstandard-us.com/assets/documents/amstd/spec/SpecSheet_4413.pdf By the way I love the look of your sinks and vanity badgergal.