No monitor is going to "tame." Some may tolerate you better than others, but they will never "tame" like a dog. This applies to all reptiles.
Having said that, if you are looking for a monitor that you could interact with, the ackies are a fairly good choice. My male is very outgoing and will curiously inspect me if I put my hand in the enclosure (sometimes he will climb up my arm out of the enclosure, so I think he realizes that my arm is a way of escape as well). The female on the other hand, is very flighty. The only way that I can see her in the enclosure is if I remain completely still so she doesn't realize that I am there. There may also be other dwarf monitors you may be interested in. Just do some research.
Argus and flavi/argus or flavi/gouldii crosses are also possible good choices, I think. I don't own one. I hope to own a single male or a pair of some type of flavi cross soon. These medium-sized monitors are said to be very outgoing, but don't hesitate to show you your place. They have an extremely strong feeding response and have no fear of people. Sometimes they can be handled, sometimes not. It depends on the individual, like with all animals. Flavi crosses are smaller than pure argus or gould's monitors, more beautiful than either parent (personal opinion), and I think more tolerable of interaction (more likely than argus). They still have the same awesome feeding response and outgoing behavior as pure argus, in a more managable size.
Blackthroats are also nice choices, but get extremely large. They can also vary on temperment as well. SHvar has a large female ionides that can be taken out of its enclosure and interacted with easily. He also has a male that is completely the opposite. I would love to own a blackthroat or whitethroat, but don't have near enough space. The same goes for water monitors, which are even larger.
Dumerils monitors may also be good for you. They are also medium-sized. They are smaller than argus, and easier to interact with usually. Ben at roughneckmonitors.com reccomends a mostly shellfish diet, which may be cheaper for you. It depends on how easily you can get crawfish and other shellfish. Others have had success on a rodent diet as well. I would suggest that you check out Ben's website. There is a lot of good information.
Remember, you cannot just allow your monitor to free-roam your house. It MUST have an large enclosure. They (all except completely arboreal ones) require a deep substrate to dig and create burrows in, as well as higher humidity and temperature than your house would tolerate. Also don't expect to be able to interact with your animal. It is a monitor. Expect no more from it and you will not be dissapointed.