You'll need a pair of pants. Your local thrift store is sure to have a pair. Look for a pair with an interesting pattern and a non-elastic waistband. The waistband should be at least an inch and a half wide. Shorts will work, too. Don't worry about the legs, you're only using the top. Check out the men's section for golf pants--they come in great patterns. While you're at the thrift store, look for a men's tie that coordinates with the pants fabric for a fun handle.
Just cut off the top of the pants under the zipper and above the crotch, tweak the seams so that they lay flat, sew across the bottom and take in the top until you have a shape you like. Stitch up a simple liner, sew on the tie strap, and you're good to go.
While you're at the thrift store, scour the aisles for interesting T-shirts. Look for soft cotton with neat designs on the front or back. It's easy to stitch these up into a reusable grocery bag that folds up small enough for easy storage and can be used over and over again. Smaller bags without handles can be made for use as produce bags as well.
Take a look at the used book racks at the secondhand store for an old hardback book with an interesting pattern or design on its cover (not the jacket.) Once you remove the pages, line the covers, add interfacing to the sides for some support, and attach beaded or wooden handles. In fact, you can probably find a purse with interesting handles at the same store!
Fun and functional zippered pouches are simple first sewing projects.While you're at the thrift store, look for a garment with interesting fabric and a zipper. Use your seam ripper to deconstruct it so that you have a nice flat expanse of fabric and the zipper ready to reuse. You can adjust the size of the zipper easily by sewing the bottom of it with several stitches to make a new stopper. Use the fabric for the body of the pouch, and you'll have a unique and fun addition to your purse wardrobe.