A bathroom exhaust fan should produce 4 air exchanges per hour. Your bathroom is 7 x 7 which is 49sq.ft Assuming an 8' ceiling the total volume would be 49 x 8 = 392cu.ft We want four complete air exchanges per hour so that would be 392cu.ft x 4 = 1568cu.ft per hour. There are 60 minutes in an hour so we divide 1568 by 60min and it equals 26.13cfm. You currently have a 50cfm fan, which is twice the size you really require yet your having problems with the mirror fogging up. I suspect your problem is not the fan. Nature abhors a vacuum therefore a fan cannot push air out of a room unless there is provision for an equal amount of air to enter the room. You can test the theory by running the shower and leaving the bathroom door slightly ajar to allow more air to enter the room. Generally they make a slightly higer gap under the bottom of a bathroom door to allow more space for makeup air to enter the room but in some circumstances that does not provide enough makeup air. The solution then is to install a duct through the wall to an adjacent room and put a grille on either side. That will allow the additional air.

IMHO it is advantageous to have the fan and light operate independently. It is often desireable to have the fan run for a while afterwards (especially after eating beans) and that way you avoid having to leave the light on also. They have great electronic fan timer switches with preset time buttons (5-10-20-30 or 10-20-30-60 minutes) that are ideal for toilet fans (otherwise known in the trades as fart fans). In order to have separate switches you will need to run an additional switch wire, however, if you are going to add a wall to enclose the toilet, it's pretty simple to run the wiring at that time. Most fan light combos have the ability to operate separately. It's also pretty easy to drop in a recessed can light and have a fan only unit.

Your bathroom is 280 CF if it has 8' ceilings. Your existing fan will completely change all of the air in 3.5 minutes. Before changing the fan, I would check a few things first: 1. Is the bath fan venting properly? Do you see it pull the steam out? Is it possible that it's clogged, a flap not opening, etc? 2. Do you have a shower head that is breaking up the water too much? I installed a water saving shower head that generated much more steam than the standard head - in part because it broke up the water more and in part because I had to boost the water temp in order to feel the hot water. I had to get rid of that water saving shower head - the extra steam was damaging my bathroom.

1 cfm per square foot. Builder grade Broan is loud. Local Orchard Supply Hardware has a display of fans, customers are able to turn them on/off. Perhaps you have a local store that has similar?