To keep life simple (and the install relatively inexpensive) then part of your solution for Freeview and satellite over coax involves a device called a
multi-switch.
If you go down the route of network cable for audio-visual signals (AV) then to decide whether you'll run a separate network for AV and one for data, or if you're going to spend a lot more to integrate the two. Data and AV over CAT cable using a balun system don't play well together. The two things are incompatible. To get AV over the same network as data you need to IP-ise the AV signals. That's do-able but not cheaply. Once you have made the AV signals in to something that will co-exist with data on a network you then have to decide how you'll control the source boxes such as a Sky receiver and the Freeview PVRs. Again, all of this is do-able but it's an added cost and complication that you really don't need for something as basic as a bit of Sky and Freeview.
So what's a multi-switch and what does it do?
An aerial signal is simple and cheap to distribute. A £20 8-way aerial distribution amplifier will give you a signal from the aerial to up to 8 TVs in the house. Spend a bit more and you get IR Pass-thru which is what you need for Sky Eye infra red relays to work. Spend a bit more and you'll find an input for a radio aerial (VHF) and then the next step up is an input for a satellite signal. Once the distribution amp starts mixing TV with Radio and/or satellite down a single coax we call this multiplexing. This all sounds great except for one problem: satellite signals don't distribute in the same way as TV and radio. That's because a satellite receiver and the dish work together, and the receiver switches the
LNB (the thing in the dish where the cables connect)between one of four different states depending on the channel you want to watch.
If you use the same method as an aerial distribution amp to distribute the LNB signal from the dish to two or more satellite receivers then sooner or later there will be a conflict. This happens when one receiver calls for the LNB one state, and the second receiver calls for a different state. The one calling for a higher state wins and the second box loses signal. That's not good. A multi-switch fixes this.
You use the same satellite dish, but the LNB on the end of the arm is different. It is called a Quattro LNB as opposed to the standard Quad LNB typically installed for Sky and Freesat. The difference with a Quattro is that it sends out all four states - 1 state per cable - to the multi-switch. It's the switch that handles the demand for the signal states from various satellite receivers. So a multi-switch will combine TV, radio and all four signal states for satellite down each and every coax cable run distributed around your house. What you do with the end of the cables at each distribution point is up to you.
What if I have just one Satellite receiver (e.g. a single Sky subscription) and want to distribute the output to several rooms?
In that case go simpler. A basic IR pass aerial distribution amp takes care of Freeview to each TV. For HDMI out of a Sky box, either go with a full balun system or a mix of direct HDMI cables for sub-10~15m lengths and baluns for longer stuff.
There are other permutations depending on whether you plan to use a Blu-ray player or go 4K or use Sky Q.