Make sure to take a handbag that you can wear across your body. This will allow you to have both of your hands free and the bag close to you. Always choose one that you can zip closed.
It doesn't have to be a particularly big bag - in fact, the smaller the better.
My 5 essential handbag items when you're on the road:
1. A pouch with lip balm, hair elastics, antiseptic cream and band-aids (plasters)
2. A pack of cards
3. A pen and a notebook
4. A small roll of toilet paper and a bar of hotel-size soap
5. A collection of unused restaurant refresher towels and sachets of sugar, ketchup, salt and pepper