Hia, from me!!! Which chicken?

What you need to do is find out where you can buy chickens and then look into the different breeds that will be available. Generally, you feed chick starter to baby chicks, grower in a few weeks, then layer when they start laying. And there really isn't such a thing as a non-flying chicken. They may not get many feet off the ground, but they all fly a little. Mine will flap and climb over their 6' fence if they really want to, though they usually don't. Probably you can find out when and where chicks or chickens are available wherever you will be buying feed, if it's like here and there are feed stores. Leghorns are probably the least friendly, though they are individuals and there are exceptions. I understand you basically have brown egg layers, though, and Leghorns lay white, so they may not even be an option.

And, to my eye they're all pretty, though I guess some breeds are fancier looking than others.

You will find plenty of basic information on this site about raising chickens. Check out the learning center, at the top of the page, for example.