OK, Let’s start from the beginning.
1: Get water moving in the tank and finish filling it up. Let's get your setup running before you start worrying about Skimmers and Rocks. Normally I would say wait and cycle with the rocks but since you already have water in the tank... Those pumps/power heads would not have been my choice for water movement; they will do since you have them.
2: Ok now for your sump. I don't know what kind of skimmer you plan on running, but a Remora or the one linked above to ebay are not nearly large enough for a 220G tank. Even both together wouldn't be nearly enough for a tank that large! Of course you could run a light bio-load and go skimmer-less. I know a zoanthid farmer who runs skimmer-less and while his water is NAS-TEE his zoas are beautiful. *shrugs* OK for a tank that large you will need a large overflow (or 2) and a decent sized return pump. I will assume you do not wish to drill the 55 so a submersible pump is in order. I would recommend a MAG18 or MAG24 with 2 - 1 1/2" overflow kits or 3 - 1" overflow kits. Or Ideally you should return the tank for a Drilled tank which would be cheaper than buying the overflows. OK, so you are going to have to divide your sump into sections for bubble control. There are several ways to do this but the easiest being acrylic because you can cut it to size and silicone the crap out of it get it to stay where you want it. Glass baffles cut at a frame shop or Lowes actually bond better but generally become more expensive if you have to pay for them to be cut. Something like this:
Or this:
The possibilities are literally limitless. Just decide what suits your needs the best and go for it.
3: If you are going to run a skimmer it needs to be a big one. There are several options, none-of-which are cheap. If you want recommendations just, ask but initially I would not worry about it. Until this system get up, running, and cycled it will be fine without one.
IF this were a 6’ long tank I would consider drilling the side of the sump and using an external pump for the return. This would reduce electric consumption and heat. I would also seriously consider (if this was a new tank purchase) trying to get a tank that is already drilled with overflows, as siphon overflows are more prone to failure.
I hope this info helps and I’ll try to answer any other questions you may have.
R-