I prefer a small cross-body burgundy-red leather bag that can be worn either cross, or as a shoulder bag by shortening the straps. I like to have my hands free.
If carrying more than basic essentials – like a cardy or lightweight waterproof etc. I carry a black faux leather small femme backpack with decent shoulder straps, that can also be used as a handbag or shoulder bag. Its not as dressy as my small leather bag but is ideal for country walks.