Well if you're going with a sump, i'd suggest doing a refugium instead. This is basically the same as a sump, but it holds filtration media such as: miracle mud, a 5-6 inch deep sand bed, LR rubble, chaeto, and other mircoalgaes. This will keep your system cleaner than anything, and is the best investment! The microaglaes thrive off of ammonia, nitrates, and nitrites, so when the water passes through it, the algae sucks those bad things out of the water, like a vampire.
I have a 75 gallon Proclear Wet/dry filter with a built in protein skimmer. I add activated charcoal once a week, and phosphorous sponge once a month. This keeps my water pretty clear, but i regret not knowing about a refugium before i did that. I'm planning on adding a 15 gallon refugium to my current setup.
From what i understand, a sump is just somewhere to store all of that equipment that you don't want crowding your tank, such as the protein skimmer, heater, etc...
General rule of thumb is that the sump/fuge should be at least 10-20% of your tank size, so with a 125 gallon tank, you would be ok with a 20 gallon fuge. However, the bigger the better. The more water you have in your system, the easier it will be to work with. With more water, you have a larger margin of error to work with. For example, if you had 40 ppm nitrates in a 30 gallon tank, that same amount of nitrates would be 20 ppm in a 60 gallon tank. This would make a world of difference in the long run.
Hope i've been helpful!
jenn