You are correct -- it is that simple: water flows into the overflow box and down, thru filter material and/or bioballs/pot scrubbers into the sump, where the pump returns it to the main tank. things to watch out for: when the power goes out, water will continue to drain thru the overflow box until the water level in the tank is below the openings on the box. if the sump isn't large enough, it will overflow the sump, since the pump won't be pumping, and you have a mess. when first setting up the system, figure out how much water will flow after the pump is off, and mark a line on the sump to be your "max. fill" line. this the line that even if your power goes out, the amount of water that will drain into the sump won't be enough to overflow the sump all over your floor. one nice thing about using a sump is as water evaporates, its the water level in the sump that will go down, not the main tank -- that will remain constant until your pump shuts off. for water changes, add water to the main tank until it overflows into the sump and up to the max. fill line and you're good.
on the return line from the sump to the tank, make sure you put a small hole in the return line if the outlet is below the water level -- some put it just below the water level in the main tank, i put mine just above the water level. this hole is extremely important! don't ask me how i know! when your power goes out, the return line, without the hole, will reverse siphon into the sump as well. it isn't pretty!
to start the siphon on your overflow, insert a piece of air tubing into the siphon tube while its in position in the overflow box and suck -- once started, the siphon will be maintained even if your power goes out.
for media, i use bioballs and pot scrubbers -- very efficient. they are in a container in the sump -- i put the bottom of that container slightly below the water level in the sump to minimize water noise. the container actually sits on pieces of pvc in lenghts that i cut put it at the right height. the majority of the bioballs/scrubbers are above the water level in the sump. the hose from the overflow box empties into a diffuser tray with many smalll holes, which drips the water somewhat evenly over the entire surface. i also use a filter mat in that diffuser tray.
if you used a 55g for the sump, you can probably utilize up to about 35-40g's as a max. level, depending the level of your overflow box in the main tank, so you would be increasing your water volume by that amount. just my opinion, but once you use sumps you won't want to be without them.