I prefer a purse that has both the short handles and the longer straps so I can do what i need with it depending on the situation. I also prefer medium size--most of the purses in the stores are WAY TOO big. I like to be able to put it in my desk drawer or in my car without it taking the entire seat.
I love it when purses have the wallet as an outside compartment--hate digging for wallet/money etc. I also like a few outside pockets for cellphone, kleenex--that stuff you need to grab quickly. Yes I am pretty picky about my purses--also has to be light. I had a shoulder issue for a while due to a heavy purse.
I am impressed by those that change their purse depending on their outfit--always wanted to do that but just can't take the time to do that. I pretty much stick with one purse the entire season so it has to be neutral and just the right size.
Vera Bradley bags are interesting because they are light and well-thought out as far as compartments/size etc but they are just not my style.