How many times have you flown, long distance and domestic? I take it at least long distance you don't fly that often?
Let me tell you the biggest annoyance with long distance is how uncomfortable it can be, though that depends on what aircraft you get and how old or new the interior fitout is.
It's okay to have anxiety about flying because of all the mishaps you read about and stuff, and sometimes I get it before a flight too. But the chances of it happening are minute. Look up the
micromort, it really puts into perspective how safe flying is. And I don't really get that anxiety while on the flight. I'm usually looking forward to getting off at the destination.
Bring something to do while on the flight. You might have a good airline and aircraft with a load of in-flight movies to choose from, but a Switch or 3DS to pass the time is a good idea regardless. Keeping yourself occupied is a good way to pass the time.
I hate overnight flights because I get shit sleep, but maybe get a prescription for sleeping pills if you're going overnight. Otherwise, if you can spare the money, pay the extra to go business if that helps make you more comfortable with the flight.