Hmm, well anything that says auto is
generally not a quartz, because it's usually short for automatic. However, if it is £900 then it may well be a quartz as Tag don't do autos at that price range. Don't buy a quartz, you will regret it because there is something special about owning an automatic and knowing that there is a mechanically beating heart inside your watch.
If you are buying one first "proper" watch I highly recommend a diver-style watch with at least 100m water resistence and a reliable automatic movement. If you are looking at Tag you clearly want a brand with some presence, so I would also consider:
Longines Hydroconquest
https://www.jurawatches.co.uk/colle...ngines-watch-hydroconquest-mens-l3-741-4-56-6
Also don't be afraid to buy used in good consition, because there are lots of cut-price watches out there where the depreciation hit is already shouldered by someone else and you will get scuffs on your new watch quickly anyway
https://www.chrono24.co.uk
Unless yo uhave a very good reason not to you should laso be using a store with 0% interest free credit because spreading a payment with no penalty over a long a period as possible is always the smart thing to do and will also allow you to raise your budget a little if needed.
Well, as you know, you only have yourself to blame because there is no logical reason anyone who knows about watches would do that unless the wife was so fixated upon it that she could literally not be persuaded otherwise (which I would like to think is unlikely once you explain to her why). If I were you I'd return it and buy her something actually worth the investment.
For that money you could have got a Rolex Oyster Perpetual or many other highly respected womens watches.