I haven't flown since 1996. And I am flying alone for the first time...?

I know there are a ton of new regulations about what you are allowed to carry on, and how big my shampoo can be, I have checked that out on the TSA website. What I want to know are, how can I not seem like the woman who hasn't flown in 13 years, and get through security gates smoothly and quickly. Also, how soon do you really have to arrive before take off? And what about those connections, do I have to go through the checkpoint again?? Thanks for your help.