I have always mixed originals with cover songs. I pick songs based on the following criteria:

1. It suits my personal taste.
2. I feel some kind of connection with either the lyrics or the writer (and usually both)
3. I can make it sound as if it was a song I was meant to do. That means I do not try to sound exactly like the original version, but I try to make sure I know the song well so my version sounds real.

Some songs I would love to do but know they just do not work for me the way I want so I don't do them.

Someone else mentioned using a cover song to get the crowd's attention before showing them your song. I have found this to be an effective way to introduce a new song to a crowd. If you can really nail the cover song that the crowd knows and likes, then you have their ears to play something new that they haven't heard. If you nail it, as well, then you couldn't ask for more from your audience (short of showering you with money, of course).

Jack
http://www.myspace.com/jackswainsongs