A satellite dish isn't going to be much use with any TV unless there's either a satellite tuner in the TV (and check that it has the Freesat EPG otherwise your significant other will have a hell of a job finding TV programmes) or you connect a Freesat PVR.
TBH though, I wouldn't bother trying to re-use the dish unless there's a good reason such as you get no Freeview signal (needs TV aerial) or your Freeview service is very limited because you're on a relay transmitter with the Lite service.
The reasons I suggest Freeview (TV aerial) rather than Freesat (satellite dish) are simple:
1) Every TV sold in the UK has a Freeview tuner. In fact, any new TV sold should also include the ability to receive Freeview HD. It's there, built in to the set, so you might as well use it
2) A single TV aerial coax looped in to a Freeview recorder and then to the TV will provide the recorder with up to 4 recordable streams for the tuners or 3 recordable + 1 stream for live TV pause/rewind etc. It will also provide the TV with its own viewable stream
To achieve the same with Freesat would require *5 coax cables, some additional hardware on the dish (an Octo LNB) or a Quatro LNB with a multiswitch, a more expensive TV including its own Freesat tuner, and 2xFreesat recorders because they only record either *two streams per box (hence two dish connections to each), or record one and do live pause with the second stream. It's messy and expensive.
Have a think about designating a space as a comms cupboard to hold any TV recorders, Ethernet switch(es) and patch panels, network hard drives, CCTV recorder, IR Relay gear and any power supplies. Leave space for a small monitor. Put some light in there, plenty of mains sockets, and a revolving rack for the gear itself to make wiring and maintenance easy. Make sure it has good ventilation. A powered fan for the hot air exhaust at the top of the space, and a cool air inlet at the bottom.
Music and audio reinforcement:
It might be the news in the morning, some music while you cook or entertain in the evenings, sports commentary or an audio book, or just some better sound than the TV speakers for whatever you're watching; but whatever it is, some form of music system is pretty-much the norm now in a lot of households after a refurb.
A single Alexa speaker or two won't really cut it, You need something with a bit of presence that will do good sound and play reasonably loud too when needed. It should have really good support for streaming, whether that's a free Spotify account or something better quality such as Tidal. Smart phone / tablet / PC control is a must for both Android and iOS platforms, and Alexa integration would be nice as well. Oh, and it should have a line input feature so that it will work with the TV too.
There are three systems that tick those boxes: Sonos, Heos (by Denon) and Musicast by Yamaha.
They're all around the same price. The Denon and Yamaha systems perhaps have the edge in audio fidelity. Sonos is still good, and it excels in terms of streaming support and the control interface which runs on any current Android or iOS devices. These are all multi-room music systems, so it's possible to add speakers or player devices and use them individually, or in groups, or as a whole house system. John Lewis does the Sonos Play 5 (gen II) for £450 if you want to see it first hand and hear the quality. There's also the newly introduced Sonos battery/rechargeble portable speaker for outdoor use.
Networking:
Ethernet everywhere there's going to be some bit of AV hardware. The more stuff you can get wired in directly then the better the network will be for those devices such as tablets and phones that can only use Wi-Fi.
Plan to use some Wi-Fi access points. These will be fed by Ethernet cable and will provide strong Wi-Fi throughout the new area. Think about one or two for outside too. Make sure they can run 2.4GHz (b/g/n) as a separate network to 5GHz for n and ac. This means any devices running on 2.4GHz won't pull down the speed of the whole network.
Lighting:
Get the lighting right and you can increase the value of a new space as well as make it a much nicer place to be.
There are two aspects to lighting. The first is the lights themselves: type, function, colour, beam angle, position, numbers etc. The second is where the art is. It's using light to create and define zones within a space, and to paint a scene to create interest and lift value, and then how those lights are controlled.
I've been in homes where it's obvious that there's been little consideration given to the lighting plan. The householder may have chosen the style of the light fitting, but then left it up to the electrician to decide where the lights go, and they've simply divided the ceiling equally and then priced for X lights across the space so that it "looks neat" but with little thought about where the light falls. The result is something like open-plan office lighting. Flat, boring and never quite the right light where you need it.
It's not uncommon then, for example, to see a kitchen which includes whatever were that latest must-have gadgets when the kitchen was designed, and where it's obvious the owner has spent thousands on flashy toys such as a steam oven or a built-in coffee machine which get used once in a blue moon, and yet they've overlooked the basics such as lighting which gets used every day.
Lighting and light control is a big subject, and there's too much to go in to in a thread when it's not yet established whether you've already done something.
* Before you ask, no it's not possible to split a satellite signal feed to more that one tuner without running in to issues with reception
** Technically it is possible to have two streams recording plus one additional stream being viewed live from a Freesat box, but the channel choice is limited to one from the same group as the recording channels.
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