Fiberglass is nasty, but really DIY friendly and can easily learned at the University of Youtube =)

I'd start with some heavier chop mat like 3oz that you can cut and lay in larger flatter areas, and then some 1.5oz mat to tear up and use in curves/corners. Get enough mat for 3 layers of 3oz in the larger areas. At that point it should be strong enough that you can easily add more layers outside the car if you need to. If you pick up supplies at fgci locally, the folks at the store will help you select the proper amount of resin to go with it... they are pretty knowledgeable there and I have even spoke to guys there that have experience building enclosures. Don't forget the respirator!!!!!

Pilot Supplies and Aircraft Parts from Aircraft Spruce

This is really good resin. Very little outgassing (smell) Great for bagging.
MGS EPOXY RESINS from Aircraft Spruce

Fiberglass / Kevlar / Carbon fiber is pretty good on ebay.

Carbon tow if you really need to strong spot.

Super light panel can be made with a layup like this...

1 layer 1 oz glass cloth
1 layer 5 oz carbon single weave
1 layer balsa wood. 1/8" thk
You can do thick panels with end-grain balsa 1/2"+ thickness (super strong)
1 layer 5 oz carbon single weave
1 layer 1 oz glass

.015 thick mylar to lay and squeegy each side and a vacuum back to pull it all together.

Look up vacuum bagging videos.

Practice on some small pieces first. Use the 60 minute hardener to give yourself a little more time.

It's going to be about 24 hours in vacuum so if you have a loud pump it may be an issue for other people in the house. My wife used to hate my little diaphram vacuum pump running all night. She'd bitch and moan for a couple of days about it. Don't try it if the temp is going to be below 75F

If you're going to go fiberglass with the cheap polyester resin...

Make your box out of wood and get the shape you want. Then coat it with fiberglass mat and resin. Make sure you use enough resin to get all the little air bubble out. Most of the work is getting as much of the air as possible out. Let it kick and then go to town with 60 grit before it gets really hard. You can knock a lot of material off without too much work that way. Doesn't get all powdery either. Stop and wait if you see the fibers tearing out of the soft resin. Need to wait until it's just a little harder. Should be where you can leave a slight mark with a strong fingernail.

One other trick for you...

You'll need polystyrene foam. The kind that will dissolve in gasoline. You shape it to your liking and put the glass and resin over it. Once you have the shape, you use gasoline to dissolve the foam out. You need to use the epoxy resin on this. The polyester stuff will dissolve the foam just like gasoline. Again... make a couple of small test piece before you go large to get the feel of it.
https://www.youtube.com/watch?v=FJYNmJOwPH0
https://www.bing.com/videos/search?q...7D&FORM=VRDGAR

also... Use gloves and at least a dust mask. fibers in your lungs is bad.

This is all excellent information, but I just don't have the time or space to do this on my own. I live in an apartment complex and they ask questions every time they see the hood up or something other than groceries pulled out of the trunk. I hate living here but it's what I've got to work with for the moment.

Bummer! I've fabbed more than one fiberglass enclosure in an apartment parking lot =) One time, management did make a fuss about it, but they had stand-alone garages for rent so I rented one for a month to complete the project... ended up being kind of a blessing, as having a shop space is a million times nicer.

If I had more time on my hands these days I'd offer to help, but I can't even find time to fab my own sub box I've been hoping to do for a year (I also keep changing my plans).

That's one of my problems... Time!

Being in management, more time is spent at work than at home, literally. And days off are spent mostly running errands and doing chores.