You will have no issues wiring things up.
Just use 14 gauge (or so) speaker wire from Monoprice and run it to all your speakers, except the subwoofer.
Use a piece of coaxial cable for the subwoofer.
The back of your receiver is very standard:
https://www.avgearshop.com/media/catalog/product/cache/1/image/1800x/040ec09b1e35df139433887a97daa66f/y/a/yamaha-379-gallery-4_2.jpg
So, you should ask if you have any specific questions, but there is nothing about the speakers or subwoofer which is out of the ordinary.
Not sure why you have a couple of Bose speakers in the room. They may go back to a distributed audio system of some sort, or may be leftover surround speakers with wires already in place at the front of the room. You would need to look for where the wires connected to them already are going.
