My biggest influences are 1) color 2) functionality 3) lining color
I won't buy a bag if I don't love the color so that is definitely at the top of my list. The bag also has to be functional. Each of my bags has something about its functionality that makes it stand out from other bags. For instance, my Parker Hippie is wonderful because it's crossbody and my Maggie rocks because she has all those compartments to keep my stuff organized. The kisslock side pockets make it super easy for me to get to my keys or cell phone, whereas when I use other bags, my stuff is a piled up mess and I often think I lost my cell phone because I can't find it even after digging through my purse several times. It somehow eludes me in my purse. Haha!
And lining is not a huge deal, but more like a perk if it's a color I like, such as PURPLE! There have been some deal breakers for me though. For instance, the most recent Bonnie line had mostly coral and green linings. I said no thanks to that.