I don't have a purse, because I'm male, but I would just add one thing to this thread on the topic of the differences between US and UK terminology.
What you are talking about would be called a 'handbag' in the UK. A purse is the small wallet type thing for ladies that holds cards and money and stuff (what would you call that by the way?). I know it's slightly off-topic, just thought you may be interested.
Let's not even think about the 'fanny pack' as mentioned by Rebarnmom