Hi, you probably already have a 15amp breaker for the circuit, so you can't go to a larger one. Doing so would probably be against code and could cause an elecrical fire.
When the halides and PC's kick on, you are drawing more than the rated watts in order to fire the lamps. This circuit is probably already close to the max (15a), and this momentary increase is enough to cause your circuit to trip.
What I would do is turn off the breaker to see what other devices are drawing from that circuit. You might have to move some appliances around to free up some amperage.
Another option is to try your ballast on another circuit, like a bathroom for example, since this probably has its own branch. If it still trips, it could be the ballast.
Hope this helps!