First piano in the family, soon.
I can pay around 9000 euros ( approximately 10800 dollars, 6100 pounds) to buy a new upright piano.
Ok, the usual I'm no expert disclaimer.
If it were the UK, I wouldn't spend anything like that on an upright. But prices vary from country to country.
Allegedly the Yamaha P121NT is, more or less, a U1 in all but case, name and price. UK street price is about £3 to £3.5k. Or get the U1 or U1N which is about £4k. [These are internet prices, a shop might cost more though, you probably need to haggle to get the best prices whatever you buy]
Why pay more? The only reason I can think is if you play and listen to another make and think it feels / sounds much better and it costs more.
But, if you're not in a position to decide on the subjective merits, I'd save the extra money for when you [or whoever plays] is.
If you're thinking this is the first and last piano you ever want to buy, get a grand piano. This is where spending money makes more sense.
That said, I would probably consider the equiv Kemble before I bought a Yamaha. Why? AIUI it has the same build quality [because Kemble make all the P121NT and other Yamahas with N in the model name, after all] but it has a subjectively better sound. Different sound if nothing else.
The last tech / tuner to mention Yamaha in here said something like "I was rarely impressed with the tone, but I was usually pleased with the integrity of the action components, the positive touch, and general build quality", so Kemble, with a different tone, might impress him in that respect too. But if it impresses you there are probably not a lot of reasons to not get one.
I don't know exactly which Kemble is which Yamaha if there is such a match, but the K121ZT looks like the U1 in size [and price] here. The price you were quoted looks a bit high, more like the price of the K131 [which seems similar to the U3] but as I said prices vary a lot.
I'd probably also consider lots of other makes too that google will find, but because of their touch and sound, which I would go and experience, not because of their name.
Beyond a certain price, [and your budget certainly is] once you've got past the ebay second hand junk, the budget uprights around £1.5k or less with the silly names that are supposed to look a bit like Steinway, Bosendorfer or another famous make, beyond those, it's pretty much subjective.
I think equally, beyond a certain budget there's not much point spending more on an upright, unless you never intend to purchase a grand piano. Otherwise, that's the time to worry about which one you buy. But that's just my opinion, others may beg to differ.