Are you willing to give me a bit of advice on how I should go about it?
No problem at all. I am also old, retired.. and my brain just won't give up even if the rest of me is pretty much a wreck.
Let me suggest you move this off the forum.. talk to me direct. rayhav@gmail.com
Some of what you ask is helpful to anybody reading the thread. So that can be public.
My first question is what type of wire should I use. I am assuming CAT6 Data cable. Are you aware of anything better?
Correct. Cat6 is latest standard.. although there are higher grades available it is not really worth the expense. Even Cat5E is still fine for most installs.
My second question is, is it worth it, to run separate wires to the TV Airport Express location and connect the Airport Express, TV or Apple TV box
or is it OK to use an adaptor at that location?
or should I just rely on the much-improved WiFi signal from the Airport Express?
Alternatively, should and can I wire the TV and Apple TV box via the two outlets in the back of the Airport Express?
If it is better to run separate wires can I use the spares on the modem as the supply?
OK.. Q2 has a lot of bits.
So firstly a bit of theory.
The correct method.. is to wire each point separately back to a common switch panel in your house. On a new house this is how you would do it. Each wire run should include two cat6 cables.. even if only one is terminated.. since the wire cost is insignificant cf the labour to install it. One will be used for ethernet and the other for phone.. although nowadays phone outlets are hardly used.. both use identical Cat6 cabling. That means you have redundancy and allows you to place routers in locations different to main point where you main NBN is setup. A Laundry cupboard or garage area is then able to have a patch panel where you patch each room back to the service you want.
Hills in Australia make neat home cabinets for this.
Hills Home Hub - YouTube
Now the reality you face.
All very simple when you start from an empty frame.. much more difficult in a house especially on slab (no access underneath) and double storey.. so no access to the interior walls.. or with flat roof for example.. any sort of out of ordinary construction.. double brick, concrete, metal etc is going to make later cabling expensive.
So at a minimum.. you need one cable run from the TC to your downstairs TV location.. if there is another spot you use network/internet downstairs.. as you indicated you have two express 15M apart.. you can cross that area and terminate as well.. In the cable run I would have 2 or 3 Cat6 cables..
You can extend ethernet with a simple switch. These come in various sizes.. 5 port and 8 port are the ones you will be interested in and cost $40 or less.. ie these are really cheap items.
The speed is 1000Mbps and even one wire is more than adequate for all your needs.. but having two or three cables from one area to another just adds some redundancy and speed if you later on need it.
This method is poorer from a maintenance point of view.. fault finding is very simple with structured cabling from proper rack or wiring cabinet. But ethernet and switches are simple and reliable.. you can keep a spare and swap them over. It is not difficult.
Taking this .. let me give you a bit more specifics.
You can run a single ethernet cable.. TC to the location where you have the TV.. get a switch.. into the switch you will connect everything. Ethernet is so superior to wireless.. you want wireless for only the stuff you carry around.. ie iPhone, iPad, Macbook. Everything that does not move.. wire it.
the Airport Express, TV or Apple TV box
All just plug into the switch. (But they could also plug into multiple ethernet ports in the wall which are all independently wired back to the TC and a switch next to it).
Hope that makes sense.
or is it OK to use an adaptor at that location?
Yes.. that is a gigabit switch.. and they are cheap as.
Alternatively, should and can I wire the TV and Apple TV box via the two outlets in the back of the Airport Express?
The express is slow.. 100mbit and you will lose one port to connect it to the ethernet.. that would leave you one port only. You will need to setup the Express for wireless in your TV location.. so your iphone can connect.. but use nothing else on the express.. wire everything to the switch. Which being gigabit is 10x faster.
should I just rely on the much-improved WiFi signal from the Airport Express?
Yes, in theory you could.. don't do it. Stuff that doesn't move.. gets ethernet.. and ALL networking problems cease forthwith. Wireless is voodoo technology. Coloured feathers and rattles have as much to do with the outcome as science. Placating the evil god of the ether is not necessary with ethernet.
is better to run separate wires can I use the spares on the modem as the supply?
Possible to do this.. since the modem is also working as router.. your TC is bridged and the other ports are free.. that should give you two or three free ports at least. However it is better to plug just the TC into the modem.. and plug 8 port switch into the TC.. and plug everything else into the switch. Up to you on this one.. if the layout is messy for you for sure use spare ports..
Summary.
Wire = good
Wireless = bad.
Wire down everything that doesn't move.
In my setup I have a modem bridged.. plugged into the phone line (due to get FTTC NBN soon.. yah!!) But that will still give me exactly the same layout.. a bridged modem..
One Asus RT-AC3200 main router.
Plugged to 16 port gigabit switch. So only the switch plugs into the main router.. everything else is plugged to the switch.. this keeps maintenance easier.
I then have cabling to several rooms of the house.. but not enough.
I still need a couple of 8 port switches or AC wireless routers (I use Time Capsules) used as switch and Wireless Access Points (WAP) to get network to rooms beyond those. I also have too much steel and double brick for wireless to get very far. Single ethernet connections from room to room suffice for the rest of the house.
Get a data cabler (electricians usually have data certificates but are often hopeless at correctly wiring ethernet.. you will need to do the best you can with people available).. to do that main run with 2 cables and work from there.
Talk to me direct about switches to buy and other gear.. also configuration of the express. Any other specifics to your home.