Speaker receiver question

[TTC1984]

Obviously, as a regular on this site, I've fallen in love with the Blu-Ray format. Last Christmas, my parents got me a speaker set, which has been much appreciated - however the receiver didn't have HDMI on it, so clearly, I'm not getting the best quality sound I can.

My question is this - I need to get a new receiver that has an HDMI port. Can I use any brand speakers on any brand receiver, or does the receiver have to be the same brand as the speakers? (My speakers are RCA, if that helps, and it's a standard set with a center, woofer, front left, front right, back left, and back right.)

Any help would be much appreciated!