Let's look at planning this first.
You've decided to buy an arapaima. First and foremost: Do your homework. Obviously, it's one of the biggest things you can buy. They grow quickly. Do not make the mistake of saying "I'll upgrade my tank as it grows." That is one of the most common errors with keeping these thigns. If you purchase a small juv fish, you won't have time to construct a proper size enclosure to house it by the time it reaches at size. Have you system up and running fully cycled PRIOR to even looking for the fish. Your best bet is to have other fish in there. Arapaima will thrive in a well established tank. They don't do well at all in a young sytem. Find out an estimated food/water/electric bill. It will add up fast. Make sure you can afford it after you purchase one. You need to make sure they are LEGAL to keep in your area. Regulations vary greatly. Just because you can get one from a legal supplier doesn't mean the fish was brought in legally or that keeping it where you live is legal. Arapaima fall under CITIES II. Several States also have specific regulations regarding them. As for other countries, I'm sure there are ways to find out, and would be more than happy to assist you with that when the time comes.
Let's talk housing: Think very, very big. I suggest no less than 30,000 gallons for an adult and 50,000 gallons for two or three. Swimming area is the key when designing a pool. Depth doesn't have to be much more than about 6 feet. I wouldn't got any narrower than about 10 feet across at any point in the pool. Corners are bad, so all edges should be rounded. Even round the side walls to the bottom. Doing that will also aide in keeping water moving as well. Substrtate should be a natural color, and fairly dark. Brown tones work best. I like to use a mix of small gravel as well as larger fist-sized stones (I'll get into why in a post about breeding.) Tank decor can be basic, but there needs to be something. I've found arapaima to be territorial during certain seasons, so having objects (like logs and boulders) aide in creating a comfortable area for the fish to live. Lighting should be from above. It's been my experience that arapaima do not like underwater lights at all. The pool should have both light and dark areas during the day. Edges fo the pool should be high. These guys are amazing jumpers, and you should consider that one might jump out of the water.
Questions? Should I go into more depth on these subjects, or move on to filters?