Best of luck with your recovery! I worked as an athletic performance coach for 5+ years, so I'm throwing in my 2 cents.
Proper recovery and continued strength training are indeed by far the most important things you can do for you ankle. But the reality of the matter is that rolled ankles are by far the most common sports-related injury, and there's simply no way to completely prevent them unless you plan on skating in ski boots. If the forces that supinate (="roll") your ankle are high enough to damage tissue, they won't be stopped or even mitigated by flexible braces or high tops.
There are a lot of wannabe experts and self-proclaimed gurus in the fitness and rehab space who claim to have figured it all out, but the data clearly demonstrates that injuries simply happen and there's little we can do about that. Research on the influence of footwear on injury occurrences in various sports reliably shows that there are no significant differences between different types of shoes, e.g. flat vs. [slightly] elevated heel, hard vs. soft sole, low top vs. high top etc. Of course that doesn't mean that you should go skating in high heels or plateau boots, but in regards to "normal" skate shoes, you can choose what you're most comfortable with. If that's a high top cupsole plus an ankle brace, go for it, but it's not necessary. You can just as well go with a slip-on vulc if that's more to your liking.
tl;dr: Wear what provides you the most comfort and confidence. It's all up to personal preference, there is no "best" shoe to prevent rolling an ankle.
Topic: questions that don't deserve their own thread (Read 207808 times)