Iguanas are great and theyre are cheap to buy and easy to find, HOWEVER they eat ALOT, tend to have terrible mood swings when they reach maturity, and when the reach their adult size they need a very tall in enclosure with UVB light, which will get be expensive.
While most(if not all) monitors also need alot of space, you definitly can choose a monitor that requires a little less space than an iggy. They eat alot growing up but the food intake does go down as an adult though it is still definitly more than any snake. And im going to have to disagree with the cat thing...
Some monitors can be trained be around other animals, but even with an iguana it is not advised. Animals should always be supervised when together and should never be left alone. You should never allow your monitor or iguana roam your house instead of having a suitable cage.
I think your best bet would be a monitor. I myself own an ornate however I wouldnt reccomend one to you since you have little experience and they tend to aggressive and get very large.
A good starter monitor would be Savannah. Theyre are cheap to buy($20-50), get to about 5ft, and are usaully fairly even tempered as long as their needs are met and you spend time with them. However they do still need a fairly large enclosure.
A timor monitor is also a good starter for those getting into large monitors.They have all the qualities of a large monitor without the size, as they only get about a foot or two. They do tend be a little more expensive then savs though($80-100)
Ackies are also great but they are quite pricey...
and the list gos on..
Whichever speices/breed of lizard you go with, just please do your homework before hand. Monitors and Iguanas require a huge amount of time, commitment, and money compared to other reptiles and are not for most people. Thats why most of these types of lizards dont make it to adulthood because people just buy them thinking itd be cool to own a big lizard, but wind up underestimating their care severly and the animal suffers.
Good luck and i hope you find a lizard best suited for you If you need other information id be happy to help.