I agree with TheinfamousJ that there are two types of travel handbag. I use both types

The first is the tiny one that fits inside a personal (underseat) bag. I use this size bag when I am travelling with carry on luggage only (ie for me that means cabin spinner plus a large tote). It needs to be large enough to fit my phone, passport, small wallet/purse, reading glasses and ideally also sunglasses. I like a cross body strap for this size bag and generally prefer a zippered closure.

The second ideal travel handbag is larger - I use it if I have checked a bag and am carrying just my handbag and a second bag/tote on board. This bag needs to be large enough to hold all the items listed above plus iPad, earbuds, cashmere shawl, a book, cosmetics pouch and 3-1-1 bag. Again I prefer a zippered closure and a couple of interior pockets, at least one of which should also be zipped. It should go over my shoulder or cross body (but definitely needs to be hands free).