Every Easter, Halloween and Christmas a young friend and I bond over cookie painting. She's 13 now so we've probably been doing it 9 or 10 years. For years we used the
Martha Stewart Flag Cookie recipe, but more recently we've used a recipe for a gluten-free sugar cookies. I've found that royal icing flooded cookies look the best and the base colors go on pretty quickly. The icing does need to dry a bit before adding layers on top otherwise the icing sinks and can and will make a mess. I've found it best to edge the cookies with icing that thicker and flood with slightly thinner icing. If the icing isn't thin enough the layer of icing on the cookie is too thick so it stays soft underneath. If the icing is too thin it can and will run. To add details to the top layer you'll want to make sure to go back to your thicker frosting...otherwise you'll have a big mess.
I've always used a royal icing(with meringue powder) which doesn't have a great taste and add a generous amount of vanilla which helps to improve the flavor. The nice thing about the royal icing is that it gets hard so they can be stacked. I love the hard/crunchy-lke icing, it reminds me of the decorated cookies Judy's Bakery in Evanston sold.
A couple of other things:
1. Do be sure to use cake decorating bags not zip top bags. The zip tops have blown out with too much pressure.
2. The icing will last a week or so at room temperature. I always keep it in glasses that have a wet papertowel placed on the bottom so the icing in the tips don't dry out.
3. Toothpicks or skewers are very useful. We use them to 'smoosh' frosting in tiny naked spots and to lift off mistakes.
Another technique that I've found to be fun and a bit easier is the
Whimsical Bakehouse chocolate technique. Basically chocolate (or faux chocolate) designs are traced onto a design that is placed below a layer of plastic wrap. Once made they'll last a few weeks or longer. If you were doing round cookies you could make any myriad of shapes. I'm not sure how one would look when placed on a shaped cookie.
Have fun!