Bricks, Masonry, Asphalt and Concrete - Attaching a plaque to stucco

I have a set of house numbers that I'd like to attach to the exterior of my real stucco home. I've made a plaque out of MDF that I'll prime, paint, and varnish, and I'll screw the numbers to the plaque. What would be the best way to attach the plaque to the stucco? I've heard that I shouldn't puncture the stucco because we should avoid moisture inside the wall at all costs. Can I use some kind of adhesive?

I would use plastic anchors and screws. Drill the hole into the stucco, inject some exterior, siliconized, acrylic latex caulk, insert the anchor, drive screws. This will protect the interior of the material from the weather. Be sure an seal every possible surface of the MDF. If it gets wet anywhere, to any extent it, will swell up like a toad.

Hope this helps.

Would I be better off simply screwing the house numbers into the stucco using the plastic anchors, bypassing the MDF plaque altogether? Of perhaps I should make the plaque out of a piece of solid wood...

Almost anything is more weatherproof than MDF. You can put a wet finger on a piece of MDF and it will swell right then and there.

Any piece of wood, painted on all sides, should do. If the rain will fall directly on the piece, it won't last as long as if it were simply outdoors under shelter. If they will look ok and won't be too much trouble to paint around, mounting them straight to the wall might be the best.

Hope this helps.