The jardini, or Australian arrowana is the smallest, topping out around 24". It is also BY FAR the most agressive and fast moving of the group, negating any benefit to it's small size.
Watch your fingers, children, and pets.
The silver and black (S. American) both grow quickly from about 4" with a yolksack to over 42", at the mentioned rate of 1" per month. A tank 4' x 2' is adequate for about 16 months, at which point they will begin bouncing off the galss wildly. They are also amazing jumpers, coiling like a snake, then exploding out of the water with deadly precision. I have been bit many times while talking to someone near the tank (I talk with my hands, apprently fingers look tasty!). You must feed these animals at the surface with bugs, or by dangling meaty foods above the water, or they will develop fatty deposits behind the eyes and not be able to look 'up' as they should. This is typically caused by people who feed goldfish. In the wild, arrowanas take insects, birds and monkeys out of trees, they are not mid-water feeders. They are quite slow and deliberate in the water, and given a large enough space, are quite relaxing to watch. I have seen them in 12' x 3' x 3' aquariums, and while their basic needs were being met, they were still cramped. BTW, an adult black is often marketed as a blue arrowana for a very premium price. Don't be fooled.
The golden, or Asian arrowana is illegal for import into the US as far as I know. It is legal in many other countries, as long as it is accompanied by the appropriate paperwork indicating it originated from a captive breeding facility. They are endangered in the wild, but several programs exist where they are successfully raised in captivity. The process however, involves a manmade lake with weirs or trees sunk into the ground to simulate flooded valley conditions. I have seen many of these in local Asian businesses, as they are considered a good luck token. Most are in 180 gallon tanks, and are horribly cramped. I have never seen one in what I would call 'adequate' housing. These fish top out around 30" and are fairly slow-swimming, similar to the silver or black, but closely resembling the jardini in shape.
Hope that helps! If you do decide to get one, make yourself a very large aquarium. It does not need to be deep, just have a pile of surface area. Something in the neighborhood of 12' x 4' would do. Look at your local pool shop for a smallish above ground pool and have it installed in your basement. Many have side windows and great filters, so this is a very real option for many people crazy enough to consider it!
Good luck,
/Kris