^^^ 'Freesat from Sky' is effectively dead. It was a service which required viewers to pay a small one-off fee for a viewing card, which would enable them to view those channels (known as 'free to view') which were encrypted (but which didn't require a subscription) in addition to the unencrypted ('free to air') channels which any generic satellite receiver could bring you. However the broadcasters (such as UKTV) who used to transmit some of their channels using the encrypted 'free to view' system have now turned off that encryption, making them 'free to air'.
So any generic satellite receiver (which includes a Sky box without a subscription) can now receive all of the channels in this list:
https://en.wikipedia.org/wiki/List_of_free-to-air_channels_at_28%C2%B0E
(A 'Freesat' box is actually configured to receive just a
subset of the most popular of those channels, although the others can be added manually. It also offers a few other benefits, such as its electronic programme guide).
None of the above has anything at all to do with 'Freeview', which is a company co-owned by the BBC, ITV, Channel 4, Sky and Arqiva (who operate the transmitters). It's entirely a terrestrial service, requiring viewers to have a conventional TV aerial (instead of a dish). The range of channels available is smaller than that available via satellite but still includes all of the most popular ones:
https://www.freeview.co.uk/why-freeview/channels
When considering a recording device you need to be aware that it will normaly record signals from the tuner unit built into it, not from the tuner in either your satellite box or your TV set. So that means that it must be a 'Freeview' recorder if you'll be using a conventional aerial or a 'Freesat' recorder if you're using a satellite dish. You can't use a Freeview recorder to record programmes received via a dish. (You can theoretically record the ouput from your satellite box using the 'external source' option on any recorder but that would mean that you could only record the channel which you were watching).
If you choose to go down the Freeview route, using a conventional TV aerial, something like this might meet your needs:
https://electrical.coop.co.uk/Humax-HDR-1800T-Freeview-HD-TV-Recorder-with-320GB-Hard-Drive-WiFi-Ready-HUM-FTA-HDR1800T-320-BK
(You can also buy that model cheaper, as a refurbished unit, direct from the manufacturer:
https://www.humaxdirect.co.uk/hdr-1800t-320gb-5547ad.html )
That assumes that 300 hours recording capacity (or 125 hours in HD) is sufficient for you. If you require more recording time, look for a 1Tb or 2Tb (instead of 320Gb) recorder.
If you'll be sticking with your satellite dish (& box)you'll need something like this:
http://www.freesat.co.uk/get-freesat/all-boxes/freesat-plus-with-freetime/314757
or this
http://www.freesat.co.uk/get-freesat/all-boxes/freesat-plus-with-freetime/316465
Whichever you choose, remember that you can top up free TV services fairly cheaply by using an internet service. For example, you can get Sky1, Sky Atlantic, Sky Living, Sky Arts, Gold, Comedy Central, Fox, MTV, Viceland, Nat Geo Wild, Fox and the Discovery Channel for £6.99 per month with a Now TV box (which also makes a non-smart TV 'smart' by adding in catchup facilities and things like YouTube).