A Balanced connection is far better to a un-balanced one, but that is out of question for you as your AVR does not have balanced out. Balanced connections use impedance-balanced lines. This allows for long cables and is important in studios and professional environment where the source could be quite far away from the amp. Balanced connections use three-conductor connectors, usually the XLR or TRS jack plug. XLR connectors are used with microphones and TRS are used for mixer inputs and outputs because of their smaller profile.
In your case, we can assume that the AVR and amp are going to be one above the other or near each other. Measure the distance between the AVR and the amp, and add six to 12 inches for flexibility. What you will need are 5 high quality RCA cables for a 5.1 set up and 7 for a 7.1 set up. If you don't get single cables, buy them in pairs and use them as pairs. For the centre alone, you may have to leave one cable of a pair dangling free. What you can also do (if it is possible), in just one pair, separate the cables so that you can use a single cable for the centre.
What you do is as follows:
1. Connect the Front L&R pre-out from the AVR to two inputs of the of the amplifier. Locate the corresponding speakers points in the amp for connection to the Front L&R speakers.
2. Connect the Surround L&R pre-outs from the AVR to two inputs of the amp. Again remember the corresponding speaker points in the amp for connection to the surround L&R.
3. Connect a single cable from the centre pre-out of the AVR to a single input of the amp. Again, remember the corresponding speaker points in the amp for connection to the centre channel speaker.
4. If you using a 7.1 system, do the same for the Rear L&R.
For speaker connection, there is no difference between an AVR and a power AMP. Locating the speaker points in the amp as mentioned above, connect them to the corresponding speakers using a regular speaker cable. You can use a 12 AWG if the distance is more than 200 feet, else a 14 or 16 AWG good quality cable is enough. I am sure you already have some speaker cables, and they just need to be moved from the AVR to the amp.
Cheers