Wired keyboard, wireless mouse. No point having a wireless keyboard when it doesn't move, unless you're that fanatical about a clean desktop.
IMO the keyboard is way more of a rabbit-hole than the mouse. I went mechanical a decade ago and there's not going back, but you're in for £80 so could be out of your budget. Either way I'd go 80% TKL or smaller. It just gives your mouse extra room on the desk. Maybe someone will recommend a good membrane keyboard.
As for the mouse, you can't go wrong with Logitech. I recommend the G502X to everyone but again, it'll sting you for £70. The G703 is an absolute legend at around £55 or the G305 for a simple, symmetrical design at £35.
Get yourself to a Currys or something so you can actually hold the mice and see what feels good. Mice are all pretty much functionally the same these days; you just need to find one that fits your hand and grip style.