I hope your cabinet-maker is comfortable with all of the following.
Glass transmits heat 'much' faster than plexiglass (clear acrylic). Glass is also much heavier. But there is nothing inherently wrong with using either glass or plexiglass. I have some positives about plexiglass:
If you live in a heating climate, the plexi glazing will save you money each month in heating and be more comfortable for your iguana since the temperature fluctuates less. Plexi also dampens sound transmission, so if there is noise in your house, it will be quieter inside the enclosure. 1/4 inch plexi is strong. Don't downsize to 3/16th's. Plex has a reputation for splitting and cracking, but this is caused by improper cutting, drilling, and fastening methods.
Clear acrylic is too expensive to use sub-standard cutting methods.
Plexiglass needs a drill bit with an unusual angle on the point. The holes that receive screws must be 1/8 inch larger in diameter than the screw's shaft (check out truss-head screws, they have wide heads), because plexi shrinks and swells as it's temperature changes, and as the wooden enclosure parts do the same. To give the plastic a chance to survive, no fastened screw may be so tight that it's head contacts the plexi. Screw down, then back off 1/2 or one turn, so that the head is clearly, if barely, off the plastic.
Plexi also needs specially made circular saws, such as in table saws for making long cuts. Their tooth angles are specific for plexiglass. Blades made for wood bind, melt, and crack the plexi. Jigsaws are very bad for plexi, although there are people out there who can make them work. But for the price of the piece, it's chancy.
Not to say it's impossible to use regular wood cutting blades. I made my first acrylic enclosure with those, since I'm a contractor, but it had a couple of annoying cracks, I had to throw out a piece, and the plastic melted where the blade entered the plexi, making it almost impossible to make good cuts.
Listen only to Tap Plastics representatives, and don't believe anything your local tool 'experts' say.
If you have a Tap Plastics nearby, they will make all your cuts and holes. If not, they can sell you the blades you need, even online, I bet.
Plexiglass is also easy to polish, when all the rubbing on it's face makes it slightly foggy in about 6 to 12 months.
You can also bend sheets of plexiglass. It is an elegant way to make a corner. It's done all the time, even by DIY'ers. This needs more researching by you to figure out how to do it. I know no one wants me to detail this technique.
Need info about proper housing designs for iguanas?
Scroll way down in this PDF to get to the housing designs section: