Sounds fun. So what do you have in mind for the plane? A pretty big section or just some flat facade?

It is expensive, but a roll of Tyvex housewrap is pretty good over a basic frame. for the frame, steal components from tents or canopies (if you live near a beach, they often have broken tent frames laying about). I also used a roll of mylar for covering a 12' PVC frame alian space ship. It glues pretty well and is VERY shiny, aluminum looking. It would need to be lightly sprayed to dull it down to aircraft wings looking metal... I got a roll cheap from a online supplier of 'growing supplies', ie garden 'herbs'. Get the thicker stuff.

Wind will be your enemy with any such large structures...

I once had a Luxor replica for a Vegas theme. For the spotlight (your hatch light) I got a cheap spotlight from HarborFreight. It was like 2MM candlewatts...with a bit of haze or fog, it really looked good shining straight up from under the pyramid.