While a member of the Pacific Northwest Herpetological Society, I had the opportunity to see the fates of many savanna monitors that we picked up as rescue animals and also those that various members kept as pets. I've also had a few myself. My impression from all of this is that savannas usually (not always) get quite docile, have a hearty apetite, seem perfectly healthy, and then die of heart, liver, or kidney failure at 3 to 4 years of age. This is quite young, and it shows that most people cannot keep them properly. Why? What are they missing out on? I can't tell you, since I do not know myself. For wahever reason, though, savannas do not seem to lead a healthy life under normal captive conditions.
Other monitors would often fare better, depending on the species (some types are hardy, others tend to keel over for no easily explained reason). You say you like the looks of savannas, look into blackthroats and whitethroats. These are supposed to be hardy animals and they have a similar appearance to the savannas. Ornate monitors are somthing else you could look into, they have that same massive head and stout body that the savannas have, although they have longer tails. Ornates are not always as docile as savannas, though.
In another post, you asked about cages and cage size. I build my monitor cages using an 8 foot cattle watering trough as the base. This is filled with soil that can hold a burrow. A 8ft x 4 ft peice of plywood is put on top of this with a hole cut out to allow access to the dirt. This serves as the base for a plywood and 2x4 box that gives the monitors the opportunity to cruise around above the dirt. I have pictures at
http://www.pizards.com/hbd/tricks.html
These are for argus monitors, but the same cages could probably serve for most other mid-sized monitors (including savannas, blackthroats, whitethroats, and ornates). It takes me about a weekend and $500 to build one of these.
Best of luck,
Luke