Well, If I were you, and I had the moolah, I would get a trio of Ackie Monitors. They are the BEST starter monitor. I dont think it would be a good idea to let it roam around in your backyard un supervised, as it would climb, or dig under your fence, and you cant truely monitor temps and what not if its outside all day. Argus and Black throat monitors get quite large, bigger then 4' LOL.
A good tegu would be a Blue Tegu, they are the smallest species of tegu, and are absolutely awesome, and can be tamed down quite well. Cage size for an adult would be 8'x4'x4' IMO. The reason for 4' depth is so you can have two feet of substrate for burrowing and whatnot, wich monitors and tegus love to do.
But yeah, if I were you, I'd get a Trio of ackies, or a Blue Tegu. Blue Tegus are great though, and more and more breeders are producing albinos now, wich look stunning IMO. Expect to pay atleast $200 for a high quality albino tegu though. Red Tegus are pretty costly aswell, a friend of mine bought a 4 1/2, possibly 5' (I cant remember exact size) red for about $300 and then sold it for $500 to some guy in Texas. The thing was a beat, very thick. Puppy dog tame though, the store that had it before my friend bought it used to let it walk around the shop, never harmed a soul, was a great dude.
Trio of ackies, or a Blue Tegu get my vote though. Just do alot of research, and maybe join
www.thetegu.com for all your tegu questions, and I meen ALL of your tegu questions.
Good luck bro!