The first thing I would do is figure out where the model balances, or in other words, its center of gravity. This is the position where you want to attach the model to the stand. (Or somewhere close to this point.)
Next go out and find a good looking piece of wood. You can get wooden plaques at any big box hobby shop. Or you can do what I do, and go to a home improvement store, and buy a piece of Oak, or cedar. Next locate a brass rod. Any Radio Controlled hobby shop will have an assortment of brass rods. Pick up something suitable, drill a hole in the model, attach the brass rod. CA glue works great for this. Drill a hole in the wooden board and you have a base.
To liven it up a bit, you can print out a decal, affix it to a piece of scrap styrene, and glue it to the board. Or even just apply it to the board if you go with a light colored wood.
I have done this for a couple of models now. If you find the right couple of tubes, you could even make it so you can take the model off of the stand.