What are best shoes to wear after a broken ankle, for both safety and to minimize swelling? Any tips appreciated!

Comfort, Stability. Great question ...Often pt will wear flip flops or other shoes that fit with end of day swelling. You want to get a shoe that protects and stabilizes your foot, like a running shoe. Consider with toy doc compression hose or bracine as well if needed at your stage of rehab.
Broken ankle. After recovery from a healed broken ankle, finding a supportive shoe is important. Not necessarily high tips but one that doesn't breakdown easily. I always recommend running type shoes because they are usually made with sturdier material compared to other shoes. Take the heel and twist, the less twisting, breakage, the better, also repeat with toe bend (less the better). Replace every 3-500mi.