I'm not really a gamer so can't hugely comment on that side of things but it's worth thinking about everything you need the PC for. For example, a 4k display will look great and give you loads of screen space for running multiple applications at the same time, however, for gaming it will require a really powerful GPU in order to run games at a 4k resolution. On the other hand, the curved monitor you linked will probably work pretty well for gaming and the relatively low 1080p resolution won't push your GPU too hard however that resolution is really low for that size of display so you won't be able to fit a lot of stuff on it when using it for productivity tasks.
Out of those two, I'd avoid the curved one unless the machine is used purely for gaming as it's just too low resolution for productivity tasks given its size IMO. 4K would work well as long as your GPU can handle it (of course you can always run the games at a lower resolution if it comes to it and get a better GPU in the future). Another option would be a 1440p monitor which is a bit in the middle of the two - Gives you much more screen space for productivity than 1080p does but won't push your GPU as hard as 4k. Bear in mind that the resolution is what defines how much you can fit on the screen at once, not the size - that 31.5" one you linked would have the exact same amount of "screen real estate" as my 14" laptop. Another thing to look at is the type of panel used - there's two main ones - TN and IPS. TN is generally cheaper and is sometimes preferred for gaming due to having slightly higher response times. IPS on the other hand provides much better colour accuracy and viewing angles, personally I only use IPS screens.
