Harmony software does it all for you
You are already doing too much thinking. Harmony has software on the web, and a downloadable version (which are incompatible, stick to one or re-do everything if you switch) that asks you some simple hardware questions. Plug it into your computer USB port and start.
It's "Activity" based. One activity for which there is a physical button is "Watch TV". You enter the model number of your display, your HT system, and your cable/sat box, and how they are connected, e.g. HDMI1, etc. It will ask how you change inputs on each, repeatedly press a button, select from a menu, etc. What box selects channels, etc. Then the software sets up a profile for "Watch TV" from a large database of equipment specs and downloads it to the remote.
Another Activity physical button is "Watch DVD" (or movie, or bluray). Enter display model number and HT model number and specify BD (I believe) for its bluray disc. Enter connections and how inputs are selected... sequentially pressing a button, etc. It downloads the profile for Watch DVD.
You can create several other activities and use the small LCD on the remote to activate them, such as listen to CD, play game console, etc. You can also enter AV receivers, etc. and how they are connected. The software does it all.
My brother did this using Harmony web software and his Samsung TV and HT C6600 and Comcast cablebox worked perfectly with the Harmony 650 right off the bat.
My brother in law didn't read instructions, tried a bunch of stuff and had problems. I walked into the trap thinking I had to change timing, etc.none of which worked until I stumbled on to adding a command to switch input back to HDMI1 before leaving Watch DVD so he'd be set up to "Watch TV" the next time (instead of D in, the original problem).
I then picked up a Harmony 650 and entered my Samsung TV, Denon receiver, Samsung blu ray, and Comcast cablebox and set up Watch TV (with the receiver/surround system) and Watch DVD (with the bluray, and Denon/surrounds). Simple questions, simple answers and it works perfectly.
Most importantly, turn off Anynet.
My brother used the web software and I used the downloadable sw. I think the downloadable has one extra command or something, but it wasn't needed. Check out Logitech's Harmony website. There used to be a tutorial, etc., and a way to find out if your equipment is supported. There was only a simple user manual, however it was enough to allow my brother to program it with me on the phone helping... The website was a mess a few years ago, with additional information scattered throughout dozens of FAQ's. But, if you don't think too much, you shouldn't need additional info.
Each Activity includes common functions on the Harmony's physical buttons or accessible as soft buttons on the remote's display screen from the diverse devices. e.g., Watch TV changes volume on the TV or receiver and changes channels on the cablebox. However, each device can be accessed in the remote for esoteric commands which are rarely used. You could bring those commands forward to the Activity's screen if needed.
Your family will have to be patient and wait for all equipment to turn on/off before pointing the remote away. Good luck.