Congrats on trying to help your boyfriend choose a reptile he will like I am however gonna bring up 2 points and then ill answer your question, both monitors and tegus are expensive and need pretty decent caging and I'm worried he's not doing the research himself I have a girlfriend who wants a gekobwho can't have one unless she herself does the reading

One last thing is please don't try to get a starter reptile.. they in my experience only get neglected after the owner has "learned all they need" and its a pitty..

Now for some info

Tegus, = are amazing lizards but do require slightly larger caging an adult tegu could need a minimum of 8x4x3. Tegus can get large to, however that's not a bad thing because as they become older they mellow out and will just relax and are not that hard to handle. They can also be housed with another tegu of similar size If you both wanted to get your own, however the caging size would need to be increased. The diet depending on the species really arnt that difficult and most are carnivores. For a first tegu id reccommend an argennteen black and white simply because they do get to a cool size and have a relaxed attitude.

Monitors, = my knowledge on ackies and timors are limited I'm more into the black throats niles and argus, and really wouldent reccommend these because of the high cost of keeping and space needed. These really should be left to those who own a house and have the funds and space to have one. I am dieing to have a nile or blackthroat but simply don't have the funds or space.

My monitor info is just an overview I have no idea of your financial situation and if u can afford it then by all means there's a lot of good info out there on them and if u choose a bigger one I could give you more info if u need it

If your looking for a hands on lizard id go with the tegu simply because they actually do bond with you and will be a hands on lizard as opposed to monitors who can be "tamed" but should never be fully trusted.

So to sum it up id reccommend a tegu, don't let the size intimidate u because if raised correctly they can be easily handled and make great pets