Monitors are great animals, but a HUGE commitment! And they need big cages. The minimum for a Savannah Monitor (can grow to 3-4 ft) is 8x4 ft floor space--not even talking about the height, especially considering they REALLY like to dig!
There's also a crap ton of really bad, inaccurate information to weed through on the internet. One good
care sheet for Savannah Monitors is this one:
http://savannahmonitor.org/ I don't know of any for other monitor species, though.
If 4 ft is too big for you, then you should look at some of the dwarf monitor species. There are a couple that won't get bigger than a beardie--though they still need a nice, big enclosure! One of these is the Kimberley Rock Monitor, or
Varanus glauerti. This Canadian breeder has a
care sheet that seems pretty reliable, as well as general species information on Kimberleys and other neat Dwarf species (including Ackies)--just click on the "Varanid Pavilion" to get to the other pages.
http://www.canadiancoldblood.com/captivehusbrandy.html Since they're less common, there's also fewer "total crap" caresheets on the net for most Dwarfmonitor species, so a google search on whichever species interests you the most should bring up more good information.
Rhetoric--If you haven't seen it already, I highly recommend you take a look at the care sheet I linked to above. As well, there's a good thread right here on BD.org with information about Savs: "Rex's Savannah monitor thread" by Monkey (linked here:
http://www.beardeddragon.org/forums/viewtopic.php?f=19&t=130652). She discusses many things throughout the thread, including how feeding rodents can lead to fatty liver disease (just like if you fed a beardie too many pinky mice). Africa has huge, and abundant, insect life, and, combined with the instances of fatty liver disease on rodent diets, it stands to reason that Savannah Monitors have actually evolved to live on a diet of really big insects, as opposed to rodents, like so many assume. It might be worth looking into, in case those mice you give it every week do wind up posing a real health risk.