Euroreef is pretty accurate on their guestimates on how much water they can handle. I'm not aware of what the CS250 is rated for, but if Euroreef says it can handle 180 gallons, I'd say you're good to go as far as skimmers go. Of course, 45 more for your sump and 40 more for your fuge, so that's a total of 265 gallons. But then you've got 200# of live rock in your display which probably displaces 40-50 gallons, so really more like somewhere in the area of a total of 210-220 gallons total water volume. So I'd makes sure your skimmer can handle that, if you dont have the information that came with it, you can just check their web site.
If you're going to have a high bioload, you want a oversized skimmer
You're asking about equipment necessary, you didnt list any lights/heaters in this last post and I'm not sure if you've talked abot them during the thread at all? You may or may not need a heater depending where you are, you might need a chiller. You probably know already, but large temperature fluctuations will stress your fish out, so do what you can to stabilize temps.
Lighting isnt so important on a FOWLR, but your fish will look better with a good light shining down.
Then I'm assuming you already have a return pump and what not since you are planning on a sump/fuge? If not, you'll need that as well!