I have an ancient dinosaur laptop running my printer. I use PronterFace to talk to my RepRap printer over a USB cable. That computer is very low on memory and not very fast. But it works fine to run the printer. The whole reason I have it is with a long print, I don't want anything goofy happening like my main computer going to sleep or maybe crashing. It helps keep the printer isolated from what ever else I'm doing on my real machine. The only thing that laptop does is run the 3D Printer, and it does that just fine.

For slicing... A fast machine is very helpful. But my dinosaur 3D Printer laptop doesn't do that. It just pulls the GCode file from my real machine. Also... opinions are going to vary, but I don't see any benefit to a LCD Panel on the printer when I have a dedicated laptop display displaying things on my printer. I'm all for fast machines, but the truth is the printer doesn't need much to control it. (But as soon as you start doing design work, and even some bigger slicing operations... You won't want to have a slow machine in the picture.)