It's ok to use Serial for the GPS, but you have to disconnect it to upload new sketches over USB.
More choices and info here.
That page is from my NeoGPS library. The examples are structures better. The example NMEAsimple.ino is close to your program.
NeoGPS is smaller, faster, more reliable and more accurate than all other GPS libraries. If you want to try it, it is available from the Arduino IDE, under the menu Sketch -> Include Library -> Manage Libraries.