If you want a bare wooden floor, seriously consider having all the boards taken up and insulation laid between the joists. Most of the cold is from draughts, which mineral wool will block as it stuffs into irregular gaps. Do not block the space under the joists as this is needed to ventilate away damp.
You can take advantage of the access to clean out the void, unblock the airbricks, and do any plumbing or wiring that you can think of, including phone, broadband, TV, alarm, speakers, and to insulate or replace underfloor pipes. You can include access hatches.
It is best done before you start laying carpet or decorating. You will never want to take up the floors again, even if they need it. This is a source of great annoyance to plumbers and electricians.
This will give you better heat retention than boarding over your floorboards, and will save you having to cut all your doors and skirtings. If you decide to lay a new floor it needs to be at least 18mm thick, and in long lengths. Most engineered floor is in small bits made of left-overs so will not span enough joists. You can relay your own, or recycled, old floorboards if you like the originality.
I would not use parquet in a kitchen as it will react badly to damp, including leaks, humidity, and constant wet around pets' bowls, and is liable to lift as well as stain.