So much depends on the style you want to adopt for your project. But in terms of materials, you can do a lot with MDF, carving and shaping. I am sure I saw some lovely 1950s kitchen pieces, including a fridge, on this forum, and I think much of this was in MDF.
Otherwise you may want to consider thin plywood, as in 1.5mm and 3mm stuff. It is very useful for lots of things. Have a look at dolls house furniture tutorials on YouTube, bearing in mind that you will want to make the items much bigger.
For trickier shapes I like using Fimo or similar stuff. There are some good videos on using polymer clay for food items and all sorts of things.