The best weapon period for taking out enemy jets is the default machine gun.
Heat-Seekers can be evaded or they can use flares to get rid of them. The only thing that an enemy can do to avoid being shot by a machine gun is be a better pilot than you, and even then, if you get the drop on them, it's pretty hard to avoid being killed.
The machine gun also kills the most quickly of any of the jets weapons. The only downside to it is that you have to learn how far to lead the enemy jet to hit them. This comes from practice, and soon you'll be able to take down an enemy jet no problem.
In regards to spotting and keeping track of the enemy, the first thing you want to do is look at the enemy jet and press Q. Then once you've engaged the enemy, stay in cockpit view whenever you can to help you aim, but the moment that the enemy moves out of your view, switch to chase camera (C) and attempt to keep them in your sights. Switch back and forth between cockpit cam and chase cam whenever you get a chance to fire at them.
If you follow these tips pretty soon you'll be taking out enemy jets like a pro.