It's a bit more like HP (hire purchase) as the 19.99 for 24 months tots up to quite a lot of cash...
Is it unlimited data or just some small amount (almost academic now I see you plan to use it at home most of the time)...
Whether it's a good offer depends on the cost of a similar (wi-fi only) iPad Mini vs 480 pounds (20/month x 24)...
I just checked and the T3 review (which marked the price in list of negatives about unit) suggested it costs 269, 349 or 429 for the Wi-Fi versions, depending on storage size (16, 32, 64 GB) while the Wi-Fi + mobile versions are a hundred quid more expensive.
I'd say it depends on (a) whether you can afford the total cost in one go (or more by spreading the cost with Three) or (b) whether the wi-fi model would be better value for money (and perhaps use it via tethering, if you have a mobile plan that allows it)...
Also depends on coverage in your area for Three signals... and just looking online, I saw the 16 GB model costs 49 quid on top of 19.99/month.
Finally there are hints of an iPad Mini v2 coming out (so you could feel a little 'ripped off' in 15 months when a v3 is hinted at, with better features, and you're still paying for this one, (+ about 150 quid on top of the price in somewhere like John Lewis, which would give you a 2 year guarantee).
If you really want the wireless + cellular, then consider the Mini at 369 from JL (with 2 year guarantee) and buy a 3 GB/3 months data SIM on Ebay for around 12-15 quid when you expect to need to use the unit away from home... perhaps. It's up to you.
(PS Double check if you go down this route that the iPad Mini isn't locked on EE {JL web site says they give you a free EE 4G SIM card - I'd avoid one locked to a network if at all possible}.)