There are an infinite number of ways to setup a reef so I won't point to any specific products. I'm also making the assumption that by reef you mean a marine tank with rock, coral displays, inverts, fish, etc. Before I even begin, you need to realize that $1000-$2000 may not get you where you are expecting with a 220 gallon reef tank build. You may be able to get started with that, but in my experience you will likely need 3x that amount to start a tank that will be stable and successful. This figure does not include any fish, inverts, or corals and assumes you have some of the equipment already.
A few things I don't see listed that I would consider a must have for a 220 gallon reef:
- RO/DI system with a mixing station setup. If you are going to do
it properly, you need to get your total dissolved solids as close to
0ppm as possible during the initial fillup, when topping off and when
doing water changes. An RO/DI system will do that for you and is more economical than buying RO/DI water every time you need it. RO/DI systems produce water relatively slowly so you will need large storage containers, pumps, and basic plumbing to set this up so the water is available when you need it. I wouldn't even consider a 220 gallon reef without this in place.
- Test kits of various sorts. I would look at master test kits made specifically for marine tanks as well as master test kits made specifically for reefs. They will test different things. There are also other test kits you will need that may not come in the master kits. Get the best kits/testers you can afford as some of the cheaper ones are much more difficult to read in my opinion. You should also have a hydrometer or even better a refractometer to test the water salinity when mixing for water changes or top offs.
- Rock, and probably a combination of base dry rock and some live rock. Rock in a reef does a lot of the maintenance work for you. You can have marine tanks with no rock, but I certainly wouldn't call those "reefs". Even a lot of fish only tanks have live rock (FOWLR). A lot of reef forums will recommend a pound of rock for every gallon of water, not all of which needs to be in your display tank. In your case, that would be 220lbs of rock. If you went with all live rock to meet this recommendation, which some people do, your budgeted funds would probably be gone, completely. Of course, you could go with much cheaper base rock but half your budget would still be gone.
- Reef lighting that will support coral life. This is probably one of the most important pieces of equipment for your coral. You need to get lights specifically made to support reef life. Your options are basically T5's, Metal Halides, LED's or a combination made specifically for reefs. For proper lighting of a 220 gallon, you will easily need almost your entire budget for this item alone and you will almost certainly need multiple fixtures. See some of the recommendations on this forum: 220 gallon lighting recommendations
- A sump to house all your equipment and probably a rather large one (55 gallon+) I've never had a reef tank that large, but all the successful ones (and most reef tanks in general) I have seen are using sumps rather than canister filters. There is just too many other pieces of equipment and media you may need a place to house. Protein skimmers, dedicated refugium, chillers, controllers, UV sterilizers, calcium reactors, carbon reactors, kalkwasser drips, additional rock, chaeto, other macroalgae, the list goes on. I'm not saying you can't use a canister, but I believe you may still need a sump for other things.
Don't let any of this discourage you though because I am not an expert, just a hobbyist. I have also seen some impressive tanks put together for a fraction of the normal costs. I would however not rush into this as you could lose some serious money doing it wrong. I would keep doing research and join some of the excellent forums out there related to reef keeping.