My main laptop has a 4k screen and my 2nd has a 3k screen. It's been a while since I last tried mania but iirc there were some sizing issues with premade skins (since people generally only make skins for HD, not UHD) but no other issues. There wasn't a noticeable difference in gameplay.
Input lag is not a thing that depends on the resolution, it mostly depends on the monitor's own capabilities (i.e. you can have low-res monitors with terrible input lag and high-res with almost no lag), as well as your PC's specs (i.e. don't bother with 4k if your computer is old and slow). They'll tell you about input delay on the product listing or box.
Keep in mind that there are general sizing issues with 4k still because most programs are not designed to run at that resolution; osu! supports it fine by default, but almost everything else will either be too tiny to read or upscaled & blurry. Even things like Steam that attract PC enthusiasts don't have high-dpi support yet. And if it's a good monitor, resolutions that would normally look OK on a 1080p monitor (like 720p) end up looking pixelated and bad in comparison, meaning if you also watch movies on it or something, you're always going to have to go for the higher quality versions for it to look passable.
I would honestly not suggest 4k unless you have a lot of self-loathing. Wait a few years for developers to catch up and for prices to go down.