At LAX, terminal 4.
AA has the First/Biz/Elite checkin counters in a "seperate" area. As you drive around the "horseshoe", its the first set of doors at terminal 4. If you are flying First, Biz, or are elite, go in these doors. If yo don't, you can simply use the other doors and walk a down to that checkin area.
I don't think I have seen the self checking machines in that checkin area, althought they may be down in the "coach" checkin area. However, I don't think you can use them at all for international. Certainly not if you check bags. I have personally heard announcements being made to that effect.
There is an "elite" security line at T4. The security area splits the two checkin areas. Each side has its own escalator, with two entrances to the security area. Once you pass the person checking tickets, all machines are for all travellers.
You won't get an op-upgrade just becasue. It will *only* happen if they *need* to move people into a different cabin if one cabin is oversold. Don't even think about counting on it or expecting it. There will be lots of Plats and Ex. Plats on the flight.