If I was doing this I would absolutely use a player rather than a computer. Why you ask? Okay, since you asked...

The computer is subject to internal processes which sometimes call an IRQ that for a tiny fraction of a second interrupt the stream of whatever is running. Even that quarter of a blink of an eye interruption is audible when what is running is a music player. An external player is not subject to that. However, you also then face the requirement of buying a high end enough stand alone player that has RCA outs because really, don't use a headphone jack if you can avoid it. I believe Matt said his has RCA outs to go to his PA system, so that model would be a great option. I'll just never forget how I went to play that gig with my friend. We started at 8. We arrived at 7:45, and we were ready to start on time. 2 speakers on fly poles, 2 power strips, his iPod, guitar and our 2 keyboard cabling as well as 2 mics, and we started. I knew about half the songs, more I was able to fake and play, but for maybe 25% I knew zero of it and faked it with either volumes off or lip syncing harmonies, and nobody in the crowd knew a thing. And at the end of the night he handed me 100 bucks and I went home. I'd do that 7 days a week if they were all like that!