Let's start with some basic stuff:
If you get rid of your Sky subscription, you probably won't gain anything from getting a Freesat box. A Sky box without a valid subscription becomes a generic satellite receiver, which will receive all of these 'free-to-air' channels:
https://en.wikipedia.org/wiki/List_of_free-to-air_channels_at_28%C2%B0E
A Freesat box wouldn't give you a great deal extra. It would actually give you just a
subset of the channels in my link above by default (although you can manually tune it to pick up the others). All it really gives you is a few additional features, such as Freesat's electronic programme guide. However if you did decide to buy one you wouldn't need to pay anyone to install it. You can simply plug it in to replace your Sky box.
For completeness, I'll mention that there's also 'Freesat from Sky' which, confusingly, isn't the same as 'Freesat'. You get 'Freesat from Sky' by paying a one-off fee of £25 to get a viewing card for your existing Sky box. That then gets you all of the (unencrypted) 'free-to-air' channels from my link above, plus a small number of (encrypted) 'free-to-view' channels, shown under 'Extra channels' here:
https://en.wikipedia.org/wiki/Freesat_from_Sky#Extra_channels
If you've got a decent broadband connection (with no data limits), one way to get Discovery is to get a Now TV box, together with a monthly Entertainment Pass. That pass gets you Discovery, as well as Sky One, Sky Atlantic, Sky Living, Sky Arts, Nat Geo Wild, Comedy Central, Gold, Fox, MTV, ITV Encore, ABC Studios and Viceland. It costs £7.99 per month, with no ongoing commitment.
A Now TV box, even without a 'pass', makes a TV 'smart', giving access to catchup services (such as BBC iPlayer) and, for example, allowing you to watch Youtube content on your telly.
With current Black Friday deal, a Now TV box costs £12.50 and comes with two months of the Entertainment pass channels included:
http://www.nowtv.com/box-bundles