If you have the space, get yourself a $25.00 bike at a yard sale and put a big wire side-saddle type basket on the rear. Yup - the big wire baskets like kids used to use in the 1960's for delivering newspapers.

A wire basket used will cost about $5.00 or new about $30.00. For around $50 or $60 you get a bike and a basket rig just for shopping and you leave your main bike untouched/unweighted and ready for your favorite use.

You can easily get from two to five full bags of groceries on this kind of rig. Need more? Throw on a full-size back-pack and load it up. More? Add a front basket.

Now, you can see that all this weight adds up. I have loaded my bike with over 300 lbs of shopping + my own weight (that's 300 lbs total, folks, not 300 lbs of shopping). For this kind of abuse, you might consider looking for and old Schwinn (even an old Varsity or Collegiate 10-speed). They had steel frames that were welded (not brass brazed) = strong.