What should I upgrade first? I just got a new basic hardtail bike. I want to get better, and it’s not the best bike, so I want to upgrade it. I was thinking about changing the gear set up to 1 and 11 speed rather than 3 and 8 speed. I go out about mountain biking twice a week, and I really like it. My budget is £250. Any suggestions?
Switching from 3x8 to 1x11 would be an expensive upgrade, well beyond your budget unless you get lucky hunting for used equipment, and may require a cascade of upgrades you hadn't planned on, which increase the cost further.

You'd probably be better off saving up for a new bike--bike manufacturers are able to get parts at much lower cost, so when you buy a complete bike, you're getting the parts more cheaply than you could get them as an individual.