Is there any certain way to dress when you're flying?

I've never flown and I am going to have a one hour flight soon with a 3 hour flight on the way back. Do you really have to take off your shoes? Because I like to travel very light, it's only going to be for a weekend and I have one pair of shoes I am going to wear with everything. They are gladiator sandals and I plan on wearing them to do everything, walking around and going to the club. They might be kind of a pain to take off but not too bad. Does it really matter? Will they pat me down at the airport? I really don't like being touched but I suppose to will do it if I have to. It's better than unneeded radiation from those machines you walk through.