Best Monitor Up to 200 Watts

You need something small....have you and your daughter go listen and have her choose....a wonderful Parent/daughter outing. Take her to lunch afterward and make a day of it.

Totem Model 1.

Von Schweikert VR-1. They are efficient, sound big and they are within your budget.

Totem Model 1 needs a lot of power for the sound to become balanced.

What does "up to 200 watts" mean in speakers?

Agreed that the Totem 1 is amp dependent, but in my experience it has little to do with WPC ratings.
That being said, I'm not sure it is the best choice for loud rock at a college house.
If it is a large space I will commit blasphemy and suggest finding a used pair of Klipcsh speakers. With a little imagination, Quartets on short stands could be considered "monitor speakers". They can be found for about $400, sometimes less. A couple easy mods(searchcritesspeakers)for another few hundred can really improve what is already a great rock speaker. Very little chance of running out of headroom, or blowing a driver. This is a recommendation for LOUD ROCK, but I really like the sound for all music. Caution, this may result in excessive partying.