Buying the ticket
I highly recommend getting the NJ Transit and "Train Time" apps. The latter is the official NY Metro Transit Authority app. You can buy the train tickets in advance -- they're not for a specific departure time, so you can figure out exact tickets you need without fumbling around on the app at the station. Both apps work fine but are not exactly the best designed, so it's just one less thing to worry about while you're juggling your luggage, etc. You can pay with Apple Pay/Google Pay in the app as well.

Activating the ticket for the train
After you buy the ticket, you need to activate it before you get on the train. You can do this for around an hour before. Note that cell reception is poor at Penn Station when you're sitting on the train in the terminal, so you might not be able to activate the ticket when you sit down on the train. It's easiest and less stress inducing to just activate it once you're in the terminal, but don't worry, if you haven't done this yet, you'll get reception once the train starts moving, and they don't check the tickets until a little after that.

Getting on the right train
Penn Station operates on a board system where the exact track each train is on is not assigned until only a couple minutes before the train arrives. So once you get to the terminal, just outside the entrance to the tracks you'll often see large groups of people waiting around staring at the screen, with groups hustling to get to the train to get a good seat once the train arrives. I'd recommend doing this, particularly if you have luggage.

Good luck with your journey!