Vans has a variety of products now some which have a lot of support. Also they seem to grip rainy and slippery surfaces very well even if they are the basic vans. I've tried them in slippery environments like amusement ride platforms in the rain and I have a bad ankle too which means I am definitely prone to falling in these environments but vans kept me from falling I did have to watch my feet when on a slippery amusement ride platform of course but the shoes did help.

These are ideal for running in a mall on the slippery floors etc.. They make special shoes for grip called the MTE line, I have 2 pairs of those now and they are insane, you literally can't fall in them.

I just wear the 'old school' ones, basic everything. I do have slip-ons and high ones with laces depending on the weather.