Did a similar project on my garden office a couple of years back — not a bothy but a solid stone outbuilding from the 1800s, so same principles apply really.
Honestly, don't skip the floor. It's tempting because it feels like the least dramatic heat loss culprit, but in a stone building sitting on bare earth or old flags, you're losing a surprising amount upward through conduction. I used 100mm PIR board under a floating chipboard deck and the difference was immediately noticeable compared to when I'd only done the walls.
The thing with old stone buildings is the thermal mass works against you in winter — the walls soak up heat for ages before the space warms up. So if you're insulating for intermittent use (which most bothies are), you actually want to decouple yourself from that mass as much as possible. Internal insulation with a decent air gap, then your finish layer.
Roof is obviously priority number one though. No arguments there — warm air rises, you know the drill.
A few things worth considering specific to stone:
- Vapour control matters a lot here. Stone needs to breathe on the outside face or you'll get interstitial condensation issues
- Lime plaster over the internal insulation rather than standard gypsum if you can
- Underfloor doesn't need to be fancy — rigid foam + chipboard is perfectly adequate
Running a small Victron system with a couple of panels on my outbuilding now, and the insulation is what makes a 200W panel actually viable for keeping the space usable in winter.
What's your floor situation currently — earth, flags, concrete? That'll change the approach quite a bit.