For the floor in the kitchen I would normally recommend cork for the ergonomic properties.
- Globus Cork has a prefinished snap together floating floor that can be installed over your existing if it's in reasonable condition.
- If your puppy is more destructive that cork can handle, which is pretty tough and antibacterial naturally, linoleum may not be a bad option.
The most durable choice would probably be a tile, whether ceramic, porcelain, stone, or clay. Tile is non-toxic generally and does not offgas.
For finishing the deck, I recommend using linseed oil, beeswax, or a low VOC whey based finish. You will have to recoat annually with linseed oil or beeswax. Products like Vermont Natural Coatings are more durable and non-toxic.
If your wood is pressure treated lumber, it may be more harmful for your puppy than the finish on it.
For more information:
Read "Can you recommend healthy flooring for a home with kids and pets?" a Q&A answered by Mari Strain.