craftgrrl | How I Recycle (sewing help desperately needed!)

I'm trying to learn how to sew. It is not a natural talent for me. At all. So far, I've fixed a hem on a curtain and turned old sheets into pillowcases. Then, I decided to turn my kids' old clothes into something fun. Mostly so I could practice sewing, but my rugrats and I also had a blast making a game with beanbags.

...So, my question is this. How the heck do I sew up the beanbags properly once they're filled? These are done, but I hate the way the edges came out. I'm working on a quilted pillow next, and I really really don't want an ugly, obviously badly hand-sewn seam showing up on the edge. Is there a trick to this? A specific stitch I can Google? Can it be done on the machine? Can it be covered? Could it be any more obvious that I have no idea what I'm doing?

Thanks very much in advance for any suggestions. You gals rock!