connecting flights? checking bags?

Having flown hundreds of connecting flights, I can tell you -- the ticket agent will check your bag to your final destination, that way the airline will take your bag off the first plane and put it onto the second plane.

All you have to do is find the gate for your next flight.

I don't know american airlines specifically so you should call the airline prior to your trip to be safe. That being said, I have never heard of airlines doing anything else, they SHOULD be automatically transferred for you.

This of course is why I fly frontier, they have great prices, little tv sets in the headrests in all classes with both standard tv offerings and movies as well (frequently included with tickets depending on where you get them and all that), and they almost NEVER have anything but direct flights. What a great way to do business.

The airline handles the luggage. You can pick it up in LAX

Ask when you check in, Theyt will tell you tell you if you have to do that or not.