Not that long ago I had the very same problem, getting a stand for my 1/72 planes for 28mm wargames.
The one criteria I had set was that the plane was at least 500mmm high up in the air, so it would easily be above any of the buildings. As at that height everything wobbles like crazy I came to use at least a 5mm acrylic rod. Anything thinner did bend too much under the weight of the planes, and anything thicker made it impossible to put into smaller planes like the PO- 2.
The base itself is a standard GW 65mm base, that is by now more metal washer and greenstuff then anything else and clocks in at 120g.
The bigger and the heavier the better, but I did not want to take up unnecessary much place on the board and felt that with that base the stand was pretty solid. It will not do well during a earthquake, but so far it has not let me down.
As for the plane, I filled up the part where I wanted to attach the rod with greenstuff and drilled a hole into it, and placing a small piece of metal at the bottom of that hole. Getting ~8mm of the rod into it, with a small magnet attached just for that little extra snap fit.