#1 - be sure to use a good aftermarket insole to replace any shoe's stock insole. Superfeet makes a great product, and it's trimmable to fit in your shoe. Foot, ankle, & knee health (in my opinion and experience), begins with proper arch support.
#2 - if you are worried about rolling your ankles, a good stability shoe like Barricade, Court Ballistec, or CC Genius are among the best in preventing rolls. These three I've found to be near impossible to roll, and in those shoes I did not need to use my ankle brace sleeves.
#3 - some will say a lighter, less stable shoe will be better for increasing your ankle strength, but sometimes that is easier said than done for us aging folks. In that case, I refer back to 1 & 2. Babolat's Propulse blends stability (although not on the level of the 3 I cite above), with a lighter, faster feel. The adjustable straps are nice to customize your heel & arch support, which is nice too.