Small room with warm steam from the shower? I would think no heat lamp required. Think of the old hotel rooms with the heat lamps in the bathroom--yes, the room was cool when you went in, but once you got the water going the heat lamp was overkill.

We installed a Panasonic fan that has light, heat and night light. I'm not sure if the main light is an LED. Panasonic fans get good reviews.

don't have a picture but since the housing is white and so is the ceiling (or will be we're redoing it) it really doesn't standout out that much...ours is set near the back wall, just above the toilet...the only cautionary is cleaning it on a set schedule, as they do build up dirt and lint from towels, ect...

First thing is DON'T listen to folks unless they are knowledgeable in that field. The person that told you to simply change the breaker is a fool! See what is actually on that circuit. Adding a 250W heat lamp will not overload the circuit unless it is close already with what is always on. You can have potentially 40 amps worth of load, it's just that not everything is on at the same time. There are no heaters or bath receptacles on this circuit, are there?