I found out that the center channel and the rears from the ProMedia system are rated for 60W with 6ohms impedance and the RF-62's are 125W with 8ohms impedance. I see that the amp is good for 140W per channel with 6ohms impedance.
Then it will work. You will, of course, want to use the automatic setup for levels and delays, though most automatic setups do a poor job of selecting the crossover frequency.
You will want to select a crossover frequency above the -3dB point of your speakers, and at 100Hz or lower if possible while doing that. With speakers that are flat down to about 60Hz or lower, usually 80Hz is a fairly good choice. I see from:
http://www.klipsch.com/na-en/products/promedia-ultra-5-1-specifications/
that the speakers appear to only go down to 100Hz, which means you probably will want to select about 120Hz for your crossover point for them.
A couple of points: It does not matter that the impedances are different; what matters is that the amplifier is capable of dealing with all of the impedances. It does not matter if the speakers are of different efficiency, as long as the level controls are capable of compensating for this for the listening position (that is dealt with in the automatic setup).
As for the power handling, there is no standardization for that, so it is virtually meaningless. And it is worth remembering that the output power listed for an amplifier is regarding its capability, not what it is outputting at any given moment. How much power an amplifier is putting out is dependent on things like the input level and the volume control setting, and as music varies, so the input level of the signal is varying, and therefore the output power is constantly varying.
Generally speaking, you can find out about how loud you can play a system by putting on music that is at a fairly constant level, and slowly turning up the volume until you start to hear distortion, and then turn it down until the distortion goes away, and you have found what is likely your maximum safe volume (though obviously playing it that loud all day could lead to excessive heat). Keep in mind, that does
NOT mean that you will always be safe with the volume control at that setting, because a higher input at that setting will result in the amplifier putting out more power.
But it does give you a kind of reference point, and if that is not loud enough for you, you either need more sensitive speakers, or speakers that can handle more power, or a more powerful amplifier. Or, if you are one of the many crazy people who literally listen at levels that are so loud that they do permanent damage to their hearing, you should learn to enjoy music at safe levels instead, unless you don't want this to be a lifelong hobby and would like to end your days with a hearing aid and even then not hearing well while using that aid.