You've asked a lot of questions! There are literally thousands of registered daylilies, and probably more that aren't. I would recommend that you spend some time browsing the daylily database to get a feel for what you like. Personally, I don't have a favorite, but I am drawn toward patterns, teeth, and beards.
Daylilies are, in general, very hardy. They will survive with little care, but thrive if given more. I'm sure there are others here who are more knowledgeable than I am, but I'm going to post these photos for you:
This is Siloam Double Classic. It's an older cultivar, so it's inexpensive. It's extremely hardy and dependable for me, and it's always beautiful. It would definitely be a good place for you to start.
(Others might recommend Stella de Oro, but I personally dislike it. It's cute, but it's plain yellow, and it's all over the freaking place.)
