Judystill... I have a woven bag purchased from Banana Republic that I have used for my summer bad the last 3 years. It has held up really well. Have a look at the material when you purhase. The Reiss one is polypropalene, no straw or raffia involved. Some are made with natural grass fibres, some with paper-straw.
If you are going to use it as an occasional summer tote and don't expect it to last years, then go ahead and get a cheap and cheerful one.
I've always loved the look. I also find a top clasp, zip or magnetic closure good to have, so personals aren't falling out when it tips over!
Lots of good bag suggestions here.