For what to run to each TV location:
1) For HDMI Baluns-->2 Cat5e or 6
2) For TCP/IP Network-->1 Cat5e or 6
3) For IR repeating, etc-->1 Cat 5e or 6
4) For future use-->1 or 2 Cat 5e or 6
5) 1 or 2 coaxial cables for backwards compatibility. You may want to consider a cable that could be used for baseband video or 2 channel stereo and RF video (OTA or cable) to be flexible.
3 & 4 & 5 could be skipped if you don't have an immediate need and the location is easy to access. If you are fishing/cutting holes etc to a location, run the extra.
I don't think you need to hire a professional if you are willing to invest some time into this and learn. If you will not enjoy learning it or doing it yourself, then hire someone, because it will take you a while to learn it all if you have not done this before.
As Chris and jautor said, the VCR and 2 channel audio will be a challenge to distribute over a HDMI Matrix switch. I have a seperate switch that distributes 2 channel audio and composite video. I do all my audio with this and some legacy video sources like a VCR. You can pick up a component/stereo matrix used pretty cheap. I have some for sale here
for only $70 which is what I used. They are serial control though, so you need a control program (I use CQC) The composite I transmit over the one extra coax cable to the TV with F to RCA adapters. I just need to switch the source at the TV to see it.
For the audio, if your Denon has A and B outputs you could use A for the Den, then B for the rest of the home audio. Run the A wires directly and the B wires into an analog matrix