Congratulations on your first flight!
Here are the answers to your questions:
1) Normally you choose the airline that suits YOUR needs - in terms of a price, route, preferences, and schedule. As it was previously mentioned, I highly recommend using aggregators similar to SkyScanner/Expedia/AviaSales.
2) Yes, you can book a hotel room beforehand - and you probably should do that to get the best price. To stay on the safe side, I'd check refundable options, in case you have your plans changed.
3)When you get to the airport (better 2-3 hours in advance, especially given this is your firs time) you'll need to pass trough security check and register your luggage. It doesn't take much time, yet there can be waiting lines, and you don't want to be late for onboarding.
4) When you land and go through the customs control, you'll see the sign where your luggage is - don;t worry about that.
Enjoy your trip!