Can a standard dryer be stacked on top of any front loading washer, or
do the washer and dryer need to be specifically listed as stackable
and compatable with one another?

Not all washers are structurally sound enough to stand the weight and
vibration of a dryer on top of them. A few years ago a friend of mine
tried doing this with a regular front-loading washer, and after a few
months it crumpled and caused an electrical fire.

I heartily agree with Pink. I have seen several stackables
disassembled and they all had reinforcing. It is there for a reason.

An inexpensive source to buy used stackables would be Craigslist.com.
If you are in a large city-- NY, DC, LA-- they are listed rather
commonly. Over the summer in DC there were about two per week!

If room in your current abode is a problem, having a professional
install a shelf to hold your dryer over your washer is a possibility.
Also, a reasonably handy person could build a stage out of sturdy wood
with reinforced joints. 4x4 legs with a 2X frame and metal reinforced
joints all around would be sufficiently over-engineered to do the job.
Check the library for books on such a project and consult a local
licensed professional for weight tolerances, clearances for the dryer
and vent, and all code requirements.