We moved into a doer upper and it took us 6 years to get round to starting the renovation, what with small children and changing economic circs etc. It will probably take almost as long to complete everything. So I think you are right to try to make things comfortable in the interim. It’s amazing how time passes while you’re thinking about things, and how long permissions, finding builders etc take. But this is good, as your ideas change as you get used to the house.
I would rip out all carpets if they are stinky, and the bathroom one regardless. Buy a pile of cheap bath mats or an offcut of Lino to protect the floor from water if it’s just floorboards underneath. We bought the cheapest electric shower we could find and installed it above the bath. Totally worth it.
We left carpets in situ where they were ok (in the main rooms) and this was a great way to protect the floors underneath (beautiful original floorboards) from builder damage. As the kids were little, it was also quite nice not to care if they spilt stuff on them!
Where the bedroom carpets had to come out, we bought Ikea’s largest, cheapest rugs, which are good value.
The kitchen had to come out immediately as it was revolting and unsanitary. We bought a basic Ikea temporary sink unit, and a drawers unit on wheels, and one of those teeny plug in double hot plate things to cook on, to create a basic temporary kitchen. Mostly we cooked on the barbecue outside though!
Good luck. It does feel overwhelming and it can feel like you’ll be stuck in a building site forever, but you’ll get there. Once you can see progress, no matter how small, it helps enormously.