Most 3rd party mice should work. But be aware that some models do not use Bluetooth, but provide a USB dongle that takes up one of your USB ports. I've used a Logitech 9-button mouse with my iMac and a dongle (since replace with a Magic Trackpad).
NOTE: I found that the newest Apple Magic Mouse 2 and Magic Trackpad 2 need to first be plugged into the Mac via a USB Lightening cable before the Mac will recognize and pair to the mouse or trackpad. Once it is paired, you can disconnect the USB Lightening cable and it works fine. I have a Magic Trackpad 2 working via bluetooth with my Late 2009 iMac.
What you don't get are some features that required extra software, not present in an older OS version.
So of you still have your mouse, you should give that a try. If you have already returned it, then of course look at other choices for mice.
Finally, as I said, I replaced my iMac's mouse with a Magic Trackpad, when the first came out, and I have not looked back. I far prefer the Magic Trackpad over the mouse. And when I added BetterTouchTool to my Mac, it allowed me to customize my gestures far beyond what Apple offered. I've since upgraded to the Magic Trackpad 2, which I use via bluetooth, but it can be operated via a USB Lightening cable too. And since the trackpad does not need to move around, having a cable attached while it is charging is not a problem.