If your laptop does everything you want to do, I would just look at getting a large monitor to plug into it and maybe a separate wireless usb keyboard and mouse.
@Casper have a look at the intel nuc. Great pieces of kit. Tiny little boxes and rapid as you like. Can be mounted on a vesa mount so very easy to fit under a desk or on the back of a screen. I’ve got one on the back of the big telly to act as a kodi box. Only a few hundred to set up so, well within budget.