Many SUV's including all jeeps except the wrangler use unibody construction, this includes subaru's and honda's and mazdas. You most certainly can attach a trailer hitch and trailer capable of hauling 500lbs to just about any vehicle. I had a hitch on a old grand am years ago and hauled plenty of things that were over 500lbs.
You need to evaluate the opportunity cost of buying a vehicle for 14ft long building supplies? How often are you seriously going to need to haul 4x8 sheets of plywood and 14ft long building materials? Which BTW I think you could fit 4x8 sheets of plywood in 4dr hatchbacks...Regardless though unless you are running a construction company, paying for home delivery or renting a truck to carry your enormous building materials will likely still come out cheaper then paying the mark up of SUV's, the added fuel, added insurance, and maintenance.
First of all, there is no point purchasing a trailer / towing capacity of only 500 lbs. I don't think anyone would go there unless it was for a very specific single purpose. (Motorcycle camping?).
Towing with unibody is something I stay away from, due to wear at pressure points/ hard braking / loads involved. I don't want to rehash the other postings made to the trailer towing with a car thread. 500 lbs may be fine, but see the note above. An older (1985?) Grand Am sounds like it may have different construction than a Honda, Mazda, etc.
I definitely have trips that can not be used with a 5 door hatchback at least once a week. This past 2 months, I have bought a tree, rented a large rototiller, purchased fencing materials, hauled compost, hauled to the dump, taken kayaks to the river, hauled cargo bicycle to/from the shop (does not fit on rack) 3 times, etc. We complete a lot of home handiwork and construction materials figure prominently. 14 ft long materials are surprisingly common, and difficult logistically at times, which is why I mentioned it. It is difficult with anything but a pickup with rack.. but can be done carefully with a regular pickup, trailer, or if thin, crossing through the middle of a van or SUV. 4x8 sheets definitely do not fit inside a hatchback (are you blowing smoke? I think 3x5ft is the limit)
When completing maintenance projects on weekends, time is very short, so renting or paying for delivery is not usually an option. I mean, why even have a vehicle, if you wanted to do this, just go carless. Deliveries / rentals start around $75 here for half day and go up.