While I don't often buy stuff from Best Buy, getting a entry level 7.1 receiver may be a good way to go. If you already have 6 speakers in the room, they should be spread out in a pattern that follows close to the speaker placement guide.
https://www.audioholics.com/home-theater-connection/loudspeaker-placement-guide
I would probably unscrew the main wall plate and see what audio connections are behind there. I expect you will see at least 12 wires (6 pairs really) connected out to the room speakers, then another 2 coaxial cables which run to the subwoofer locations on the left/right of the room.
I would pull off the left/right locations as well to see what was connected behind there. It makes ZERO sense that there are 5-way binding posts (normal speaker connections) at the wall plates, but it is something I might do if I started with in-wall speakers but wanted to go to floor standing speakers later. I might wire the in-wall speakers in series with the wall jacks. So, maybe those come from the main left/right speaker locations.
How to check?
Get a short piece of speaker wire with two conductors. You can use an old power cord and cut it back if you have that around. Connect one end to the binding post on the wall. Red & Black. Now, on the other end of the wire, tap it to a battery. A 9 volt battery works well. If someone else is standing next to the speaker that you believe you connected to, you should hear the speaker make a small popping sound as you connect/disconnect the battery. It won't hurt the speaker.
Repeat this process for all the speakers to ensure they are all labeled correctly and wired properly.
At the speaker connections in the corner, see if you connect the battery there, if it affects the in-wall left and right main speakers. As I said, if it were me, I might connect those in series so that I could add good floor standing speakers in the future.
Once you are pretty sure of things, then you can move forward. You can pick up a entry level receiver from Best Buy, or check out Accessories For Less for some options as well. The receiver you listed is a perfectly capable entry level receiver...
https://intl.pioneer-audiovisual.com/products/av_receiver/vsx-834/specification.php
It has 4 HDMI inputs which should be plenty for a typical setup.
Speaker wire is probably overpriced at Best Buy, so get it from Amazon or Monoprice if you can wait. Realistically, you don't need much speaker wire. Just enough to get from the receiver to the wall. Be aware that your wall connections unscrew. You don't need ANY banana plugs, but they make installation much, much easier. Once again, if you can wait, Sewell Silverbacks are a great value and work really well. Beyond the 12 for your wall connection, you may want to get another 4 to 12 so you can connect to the back of the A/V receiver.
Banana Plugs:
https://www.amazon.com/Sewell-Silverback-Banana-Speaker-Connector/dp/B0072KOHQ4/ref=sr_1_3?crid=2F14WVVAY64AF&keywords=sewell+silverback+banana+plugs&qid=1563381243&s=gateway&sprefix=sewell+silv,aps,125&sr=8-3
Speaker wire:
https://www.amazon.com/Performance-Gauge-Speaker-Oxygen-Copper/dp/B01N4BIXDX/ref=sr_1_4?keywords=50+feet+speaker+wire+14/2&qid=1563381278&s=gateway&sr=8-4