As someone who has had bad ankles in the past, here are my experiences:
The first option is to wear heavy boots. I used to do this. The downside is that they are heavy, stay wet, and restrict some of the flexion/extension of the ankle that you like to have. The upside is some protection from rolling the ankle too far laterally that can cause injury.
The second option is to strengthen your ankles enough that you can wear light meshy trail running shoes. I have done this over the past couple of years. They are lighter, dry quicker, and have little restriction in ankle movement. I think they cause fewer blisters. It is also my opinion that a low-profile trail running shoe lessens your chances of ankle roll about as well as a supportive boot. The main downside to this option to me is that you do need to strengthen your ankles before you start wearing them on the trail. I think running in fairly minimal shoes before using a low trail runner works pretty well.

