Is my new monitor tripping my AFCI breaker?
The concept of an AFCI is to sense an ARC occurring in a circuit. This can be caused by almost any dry set of contacts or any loose fitting in a circuit such as a poor connection at a receptacle or even a lamp loosely screwed into a socket. I can't think of anything in a monitor that would trip an AFCI unless you have a separate power supply for the monitor and a small arc may be occurring randomly in it.
Verify that the power supply is making a solid connect at is receptacle and check where the power supply cord is plugged into the power supply module.
Then again it may be a small arc in the power module itself. You might try and replace the power supply to see if the random trip is corrected. If that does the trick you usually can return the original power supply under warranty.
As far as a surge protector you would be better off using a small UPS and power your computer and it's monitor from it. A UPS because of its construction not only prevents sudden outages knocking you system offline, but it is actually a very good surge suppressor.
Hope this helps and good luck.