What size wire and breaker should I use for a small one bedroom cottage?
If I were you, I'd go as follows (assuming US split 240v)


Run 8 gauge THHN from your main panel to your subpanel (in buried conduit) and use a 50A breaker in the main. Run 4 wires so you get 240v and ground. Should be more than sufficient for anything you can throw at it and you can always expand if needed. Be sure to ground your panel to a grounding rod while you're at it.
Run your lights on a single 15A breaker. Makes adding lights easier, it's cheaper (14 gauge wire and 15A switches, and don't forget to add neutrals to the switch boxes!) and you won't be in the dark if you blow a breaker in the subpanel
Run a 15A breaker to a single dedicated outlet for your AC. It's overkill, but I'm assuming you have a 5k-6k BTU window unit. That's 6-7 amps, which is a lot to share with other outlets, even on 20A (especially with 2-3A for a fridge). If you ever decide to upsize, you have no worries about rewiring it either.
Run the rest of your outlets on one 20A circuit (12 gauge wire). Don't skimp and run them on 15A because you have a lot of 14 gauge wire. You'll regret it the first time you pop that 15A breaker.