I can tell you that at present moment (weather here in Boston hasn't really gotten that hot - still in mid-60s) the three shoes I'd rescue in a fire are:
1) Metallic ballet flats
2) Black airwalks (a converse knock-off) - I wear these a lot on the weekends in particular.
3) Hmm... the third one is tough. I would need one pair of heels, but it's a toss-up between my nude round-toe pumps, my tuquoise suede sling-backs, and my red patent round toe pumps with ankle straps. What all three have in common is that they aren't boring and predictable.
But if you're talking summer, then my list would be different. It would include a pair of white flat sandals and a pair of white sandals with a heel. The third would be a second pair of flat sandals in a metallic.
If you're talking fall/winter, then my list would be a pair of brown or black ankle boots, a pair of red ankle boots (wish-list item), and a pair of knee-high boots in wine or some other neutral color. It would be hard to limit to just three though... because I'd probably need a pair of dressy shoes for holiday occasions... and I'd want the boots both with and without heels!!
I'd have a very hard time limiting it to just three..... but hopefully, this gives you an idea where to start!! I would say definetly consider metallic or red shoes or shoes in a bright, signature color (fuschia, aqua, yellow... whatever you like). They are more versatile than you would think.