€700 seems very steep. I'd definitely get a second quote. Depending where you are you could just use a pair of rabbit ears ( works for mine). You'll probably need a new lnb on your dish (and an installer) but it's mostly labour you'll pay for. The lnb are fairly cheap.
https://www.freetv.ie/twin-lnb/
With a combo box that combines satellite and terrestrial channels you can record on the one box. I hooked an old laptop hard drive up to my box but many come with a hard drive installed. As an example this is a widely used box. No idea how competitive a price out is but you get the idea.
https://www.satworld.ie/zgemma-h7s-4k-uhd-500gb-hdd.html
I think it's definitely worth a second look. Depending on your viewing habits and how much you like to customise it could mean a small upfront cost (much less than €700) and zero monthly cost there after.
As for definitions, my rough understanding would be:
Freeview (free to air): UK terrestrial TV received in the UK via an aerial. Not really available in Ireland. Outside of a few small pockets. It will cover your BBC's, ITVs and channel 4s plus a range of specialist channels.
Freesat: similar range of channels to Freeview - though not exactly the same. It's transmitted on the same satellite as Sky. If you've ever explored the "other channels" section of Sky you'll find them there.