For most applications, printing at home is only best for the convenience. You will get consistently better results by using a good lab. And when you figure in the price of good quality inks & papers, it's probably cheaper to use the lab anyway.
Unless you specifically sign away the rights to your images, they are still yours. Having them printed at a lab does not relinquish your ownership of them (but be sure to read the fine print if you are uploading them to a site for hosting/printing etc.)