I second or third the idea of allowing plenty of time. Time to get to the airport, time to get through security, time to get to the gate, time between connections. In general, time for things to go wrong, like forgetting a last minute packed item on the kitchen counter, or a long TSA line, or a snafu with boarding. I personally don't have a problem with cutting things close, but I'm not as concerned as the OP; if I were I would allow extra time.
Try to treat the whole thing as a humorous Monty Python style quest rather than a Hunger Games competition. Other people will be stressed out and in a hurry and worried and anxious; if you let it flow like water off a duck's back then you will do yourself and them a favor. You might even get a thank you or a smile in return.
If you want to bring anything that might even be questionable in your carryon, you can check the TSA website about what is allowed and what isn't. It's quite comprehensive and fairly specific. If you're not sure, put it in your checked luggage.
When you go through TSA, you'll need your ticket in addition to your license/passport. Have them both out and ready to hand to the first agent you see while you're in line. The TSA agent and the people behind you will appreciate it.
TSA in general is easy if you're relaxed, friendly, polite, and respectful. I'm sure TSA agents have bad days, but those folks and days are few and far between. Every TSA agent I've ever interacted with has been professional and helpful and courteous to me. Even the one who had to do a full body pat down the time I lost my driver's license on vacation.
Bring something to distract yourself on the plane if you're worried about the flying part. A book, a movie, a computer game on your tablet, whatever.
If you have a choice, try to book on a newer plane, like a 787 or an A350. They have some comfort and safety features you might like, especially better pressurization. I think a lot of the newer planes also have seat back video entertainment like movies and TV. Bring your headphones (standard ones with the small headphone jack like in laptops or cell phones) if you want to use this option and don't want to buy a pair from the airline or are worried about ear germs.
You should be able to bring your own food and beverage on the flight. Lately they hardly give you any food, so if it's a long flight or you don't like what they have, it's good to bring your own.
I personally like aisle seats so I can get up whenever. If you might get claustrophobic or antsy in your seat, getting aisles are a good choice. If extra leg room might help, you could see about booking or volunteering for the exit row seats.
If you'll get antsy waiting for people to get off the plane, try to get a seat towards the front. That wait is the one thing that bugs me about flying.
Personally I don't even check luggage anymore - I just fly with a backpack. If you decide to travel without a checked bag, that means it's cheaper, you have one less thing to do when you get to the airport, and one less thing that can go wrong at your destination. Bags are rarely lost these days, but they can be damaged and always take time to get to the baggage claim, and can be mixed up where other passengers take yours. Traveling in a backpack does come with tradeoffs (mostly having to find a laundry every 4-5 days), but I find it's worth it.
You can usually find the answers to any TSA or airline or airport questions ahead of time on the internet. Maybe game it through in your head ahead of time and think about what questions might come up and be prepared.
Since you said your back was sore, you might consider getting a neck travel pillow. Might help, might not. They'll probably sell them in the gift shop at the airport.