If you use those elastic ankle support sleeves and certain ankle braces/ankle supports with laces, I suggest getting some heel slips for comfort. It will help to offset the space difference of having fabric under your foot but nothing on your heel.
For sports, the ankle sleeve/brace will be bulky. Loosening your shoe laces to fit it usually fixes it up nicely. I also find I tire easier without the heel slip if wearing a brace (possibly because my foot is rocking back and forth to deal with the space difference?). For sports, I'd suggest the lace up ankle support but the neoprene ones will work fine. For regular day, you might be able to find a neoprene ankle sleeve that might fit decently in dress shoes. If not, you might want to consider just buying looser fitting dress shoes or loafers to accommodate it. I wore one underneath dress socks before no problem. Was snug, but wasn't horribly unbearable or obvious (assuming your pants covers to the shoe).
I used to wear ankle sleeves the day of playing sports and sometimes the day after if my ankle felt tired/weak. I rarely wore it outside of those time frames. I used to be prone to rolling my ankle, but after reading this thread I just realized that these last few years, I haven't worn the ankle sleeves when playing sports.
I've also been told wearing shoes with ankle support on a regular basis helps as well. This might not work for dress shoes, but perhaps wearing basketball shoes on a regular basis/for sports could be beneficial vs regular runners.
I think ankle sleeves range between $10-30 bucks. Lace up ankle support 30-50 bucks. I bought mine years ago, so no idea on current prices. Sorry. These may interest you:
http://www.amazon.ca/Airflow-Support...=ankle+support
(Daily work one? This one seems a little flimsy for sports even though the pic shows a soccer ball)
http://www.amazon.ca/Shock-Doctor-Ul...=ankle+support
(Similar to one I use for sports)
Don't have these ones, but they look close enough to what I used to use.