My résumé has references upon request. Should I give out references to an employer I am not that interested in or hold them for the best offers?

Hold them until the prospective employer asks for them. You must remember that any reference you list on your list of references is assumed to be positive - that's why you listed them there. But that is not where the prospective employer stops. Ever wonder why an application will ask you the question "To whom did you report?" That is because those are the most important references (listed on your sheet or not) that a prospective employer wants to speak with. Just food for thought - your reference list is nice, but it is not the end of the road for a prospective employer....