All Altra shoes are Zero Drop=heel and toe are the same height. Get the softest shoes you can find and ones with a wide toe box--assuming your feet swell a bit towards the end of the day; a full day of standing on my feet coupled with sitting in front of a computer screen is not healthy for anyone, especially those of us with PD or MS. Merrell makes zero-drop shoes as well. Don't order the shoes online before trying them on in the store first. REI carries both of these brands.

Also, my cardiologist recommended I wear support socks--takes a while to get used to putting the on, especially for those of us who have lost strength and touch due to Parkinson's. Your shoes may not be the main problem.
I found that Sockwell makes some of the best on the market. I use their medium compression, knee-high socks, although they come in no-show and calf high as well. If you find that the socks are too binding, you may want to experiment with bunion socks which separate the big toe from the others. With my toes spread out, I don't even notice that I'm wearing shoes or even have problems. Hope this helps.