The cat-6 cables, which you can buy pre-terminated from Monoprice, are to save you from cussing up a storm in 5 years.
About 10 years ago HDMI didn't exist, now it does... If you didn't run HDMI 10 years ago (because it didn't exist) then you would cut open your walls today to run a new HDMI cable.
So, what you want to think about is not what you simply need 'right now', but what you want to put into the wall, since it is incredibly easy to do right now, that will give you the best long term solution and cause you the fewest headaches in the future.
That's what the Cat-6 cable is for. There are dozens of uses for that cable, but one of the biggest is that should your HDMI cable fail or break, you can get conversion boxes to carry HDMI signal over the cat-6 cable without any problem. Moving forward, it is likely that we will see new formats that replace HDMI or enhance upon it further which makes the HDMI cable you install today obsolete in 3-7 years. Considering this, do you want to put something in place today which protects you for the future?
If the answer is no, then just run the one HDMI cable and pray.
More likely the answer is yes, and the minimum cabling recommended to do this is that HDMI cable you are already running along with 2 pieces of cat-6 cabling.
If you really want to protect yourself, then run 1" flex-conduit as well, or even instead of, the cat-6 cables. That way, in 10 years if you need to get a new cable to the projector, you could just run it through an existing pathway.
But, whatever you do, you want to ensure that you are protected moving forward, and HDMI does not provide that protection, the cat-6 cables do.
Depending on the speakers you are using, you may choose to use wall plates or not - it is up to you. Wall-mounted speakers generally are wired directly into the speaker wire and that passes through the wall to the receiver. Floor standing speakers often use wallplates with 5-way binding posts on them to make that connection to the receiver. There is no 'right' or 'wrong' way to do this, but you want the wire run where you need the speakers, and you want plenty of slack on the cables at the receiver, OR you want to put a 7.1 set of connections on the wall at the receiver.
Oh, and if you insist upon the VCR and your receiver is the TX-NR809 then you just need to use composite (yellow) video and analog (red/white) audio RCA cables from the VCR to the receiver.