Dolphygyrl gives a good suggestion. You can do a simple overcast stitch that would be pretty effective without dropping the cash for a serger.
I have a Singer Serger that I'm quite happy with. I am mostly a quilter, but I do make other things every now and then and it has come in very handy.
Another thought would be snipping the edges with pinking shears to reduce fraying.
Good luck with whatever you decide!
