By foamboard - do you mean foam core (two bits of paper/card with some styrofoam in between) or board that is foam (pink or blue insulation stuff)?
If it is the foam core - regular white glue works fine with it. As does a variety of other common adhesives which work on paper/card. If it is the insulation - you will want to look at specialty adhesives that are designed to glue foam together (can normally find some at RC hobby stores as well as in DIY stores).
You might consider looking around for a supplier of thicker plasticard though. I find that it is just a heck of a lot easier in the long run than messing with foam on projects like this. If you use an industrial plastic supplier - it will probably cost about the same as the foamboard you are thinking about using.
When it comes to gluing plasticard to stuff that isn't plasticard or hard styrene plastic - superglue is your best bet.
In terms of sandable putty - lots of them, sort of depends on what you are doing with it. If I need a lot of putty - I use Bondo. Dries hard, sticks to most things, paints and sands well enough. If I am filling seams between two plasticard joints (corners for example) - I use white or green putty made for models. It is a bit like really, really thick plastic glue - so it bonds permanently and has the same properties as the plastic. If I need to fill smaller gaps in something which is not plastic - an A/B putty like Apoxie Sculpt works well enough. Sticks fairly well, and you can sand it when dry. It is cheaper than things like GS or Milliput. GS generally doesn't provide a sandable surface when it cures - so I won't use it for mechanical builds.
Once I get everything put together, if there are things like styrofoam that might react badly with spray paints - I seal the whole thing with Future through my airbrush. It is cheap and provides a fairly durable bottom coat. Couple thin layers and then prime and paint like normal.
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