Hi! i’m trying to design a 3D printer with a frend and was wondering how fast the printer head has to move? We’re trying to decide wether to do the x/y axis with a belt or a screw.
The faster, the better. You should plan for 150 mm/s nowadays but can go above that. I wouldn’t even think about a screw based solution. Waste of time IMHO. Will never get your printer up to speed 
The standard is belt for x and y where you have a lot of movement and screw for z where accuracy of level height is important.
The #Makibox uses leadscrews, for example.
Actual print speeds of 50mm/s are tolerable and will often yield a better quality than speeds over 100mm/s, but travel speeds should be as fast as possible to reduce ooze and waiting times.
I’d recommend belts as well.
Trinty labs Aluminiatus also uses long pitch lead screws. Their blurb claims 390mm/s.
Ofcourse it can be done with lead screws. But think about the mass you are turning and what stress it puts on the steppers when accelarating/decelrating. High max speed there comes at significant time spent on accelerating/speeding down. Wouldn’t be worth it IMHO.
I also suggest belts. However, keep in mind that the best belts are made to change direction (like GT2 belts). Timing belts are not optimized to go in both directions so an XL belt, for example, will have more backlash. So not all belts are equally good. Some of the newer printers use fishing line as belts but don’t know much about that personally.
Yeah, I was just trying to figure out how to get the backlash away
Large pitch ball screws. Just because I don’t see many people doing it! (But the more practical approach is belts)
Large pitch ballscrews with suitably (over)sized direct-coupled servos! Forget steppers if you want performance.
Large water-cooled linear motors with glass encoders! Forget servos if you want performance.