Mouse and Keyboard is very well supported in Linux, it doesn't matter if it is wireless or not. At least if it concerns normal plug-and-play / out-of-the-box behavior. If the manufacturer provides special drivers on top of that to configure rare unusual things (like making the mouse glow a different color), then often Linux drivers fall short of that and only support the "normal" things you can configure about a mouse for example. That includes of course remapping buttons however you want, and also setting acceleration, speed, and often DPI if possible (though I believe no standard way of setting DPI exists in input drivers, you have to check for special drivers like razerd or for DPI hardware switch below on mouse).
I would however try to avoid actual Bluetooth devices (hard to find anyway). Historically it has been quite klunky how Linux handels Bluetooth, and sometimes you get very high delay or even devices not pairing or disconnecting often. I don't think the situation has really improved much the last 15 years.
Don't use wireless if you have no good reason to, no matter the operating system. It is just an additional source of error. It increases latency and it can even cause random lag. It can be so and so, impossible to say. I have had very cheap devices work almost flawlessly over long distances, and expensive devices had issues, or vice versa. Plus you have to consider that both DPI and Hz eat a lot of bandwidth, so if both values are set very high it could choke on a wireless connection and you rather need a cable. I don't know if wireless has really improved that much the last 10 years, and it seems to remain a total mystery what particular tech manufacturers are using to mend known issues and what downsides it can entail, especially in the very fine-grained details that average customers just don't notice.
I would personally go for any sort of heavy oldschool cabled keyboard that has sturdy buttons and just feels right. It doesn't have to be spring-loaded, only the beefy old style. I mean you notice it immediately if it is good for touch typing, so actually trying it out in person, that's all that counts. Try computer recycling, they usually have a wide array of keyboards there very cheap. If you got a top 6% rubberpad-actuated vs. some random spring-actuated keyboard, I think the winner clearly is the rubber pad. It is much more difficult to try out a wide variety of spring-loaded keyboards in person, so it is equally as much harder to get an exceptionally good one. There are also notebook-style keyboards with the skissor switch mechanism (very flat keys, but it is also rubber pad). I really like those as well, and you don't have to try as many to find a somewhat good one. But I wouldn't say that they are inherently better, just as sping-actuated keybards are neither.
For my mouse I still use an old Deathadder, it did cost 70 Euros back then, and I can only highly recommend a super-expensive quality mouse like this with 1000Hz at least and DPI must be settable to as low as 400, which would be perfect for someone playing on a quite low sensitivity. I use DPI 900 on sensitivity "3" in Xonotic, with acceleration or deacceleration totally disabled. You want at least 250 IPS (it is conceivable that you can fling from your arm+wrist faster than 6 meters per second, but it seems like an impossible use case), this is the most important thing. My Deathadder has 450 IPS, I don't know if that much is really necessary (but since IPS is the most important value in a mouse, having known only 450 IPS at home, I would be very hesitant to go lower). When I used a $2 mouse a year ago, I was just surprised how accurate it was, virtually the same as Deathadder. But it has only like 50 IPS, so it would fail if you moved it too fast. I say this, because cheap gaming mice probably have improved dramatically over the last 10 years, and as long as you get the IPS and Hz then nothing really matters much. Being able to set very low DPI is a sign of quality, but not really required. Shit mice will only list a ridiculously high DPI value but not list a IPS value, anything that doesn't is garbage (sometimes you have to find out the IPS value by googling the particular chipset inside the mouse, or it will not be mentioned on Amazon but only on the manufactuer site, and it might actually be decent, but usually IPS value is not listed because the mouse just sucks). If your DPI value is totally ridiculous like 20000 DPI (not 2000 DPI) and you cannot set it lower, this will actually make your mouse perform worse from the high DPI ... unless your mousepad is only 1x1 inch large. Running mice at only the default 100Hz on the other hand is actually not that bad, but I would say it is quite possible to notice the difference, even if it is small ... plus most quality mice have this option, so why not go for 1000Hz?
In hindsight though, one of the huge things I would now rather want to check, is how complex the mouse is build internally, so that it can be easily repaired and that it will not damage from the repairs. Because believe it or not, $100 mice break just as fast as $2 mice, it is total bullshit that they last 10000 billion clicks. So wasting $100 each year or two on a mouse is pretty damn stupid. In cheap mice there is only a single chip and a single PCB with standard buttons, with everything locking in place and a single screw, which is perfect for repair. But expensive mice tend to have multiple PCBs, many single components like transistors, ICs, caps, etc and many screws that can break plus brittle cables connecting the PCBs internally. This totally sucks for repair work. What you want is to be able to buy a cheap $2 mouse, and then just scavenge it for buttons and cables without breaking your expensive mouse by the dozens and dozens of disassemblies required over the next 10-20 years. What tends to fail after the buttons is the outer plastic and the plastic that presses the buttons wears down so it won't work anymore. You can fix this with super-glue and baking soda (instantly cures). In an expensive mouse this is really important to consider. So if there was an inferior Chinese mouse on Aliexpress with less buttons, going for the "cheap style" built quality, where everything is single-chip and single-PCB ideal for repair work, given that it just had enough IPS and DPI settable around 1000 or no more than 2000 fixed, plus it was cheap like $30, I think I would rather go for that.