If we like the look of the plain stucco finish, we can just leave it that or do we have to seal it with veneer or paint?

If you like the look of the stucco - simply seal it every 3 years with an Organic Masonry Sealer. Make sure the oven is super clean an free of smoke / soot as you would be sealing those in.

Here’s a great sealer -

http://store.brickwoodovens.com/eco-advance-organic-masonry-sealer/