Print speed, stepper motor size?

I am re-purposing a DIY mill to a Repstrap, so far it prints, but the quality is not as good as the pictures that I have seen.

The printed output has bad quality when a line starts and ends.
As my machine is ballscrew driven with a cheap stepper motor. The max speed (for not skipping steps) I could achieve is 30mm/sec, acceleration 100, jerk 10.

I am not sure if the slow printing speed and acceleration and the quality is related or not, but I am planning to replace the motor anyway - because it prints so slow.

The steppers in used are 2nd hand parts, I couldn't know what the torque is. It's about 6ohm per phase.
Could someone who had experience in ballscrew mechanism throw me some ballpark number what kind of motor I should be getting (torque?), and what is the max speed I should expect?
I wonder would a NEMA 23, 3A, 1.5NM static torque motor give me like 100 or even higher speed?
My ballscrew: 5mm thread, 15mm diameter.

Or should I just consider changing it to belt-driven...

Maximum speed will depend on the TPI/Pitch of the ball screw.
IF you're stepper have enough supply voltage (often not the case) they should reach about 1000RPM, but they will have almost no torque at that speed. So the tightness of the gibs on the machine come into play.
Acceleration might improve with larger steppers, but it'll be limited by the weight/inertia of the Axis. It's also likely with an accelleration that low, increaseing the speed won't be a big win.
Mills just have different design compromises than the typical printer.

30mm/s should be more than enough for a quality print, the acceleration might be an issue, but you might want to show some pictures of your issues and see if people can suggest solutions.

Ballscrew thread pitch is 5mm.

print_screw: is a screw for printable PCB vise.
* The start/end point is messy. The picture is after the clean up, I filed some extruding bits.
My retraction settings is 0.8mm, J head 0.5mm nozzle. I print both of them at the same time, almost no string in between.

print_wade_block.jpg:
* Red Area: At every corner (where it decelerate), it's not a sharp corner as you can see but rounded with a blub.
* Green Area: Along the line there are random blubs, ABS filament quality or temperature to blame?
I am using a direct drive extruder. I wonder would the slow printing speed which induce a slow extrusion speed and hence the motor is not turning smooth enough (not enough resolution) affecting the printing result?

The screw looks like you are missing steps on the retract, it's normal to get a small blob where the loop starts, voids like those on the screw are more commonly caused by the retract speed being set too high. Missing steps are hard to see and usually result in not quite enough filament being put back into the nozzle after the retract.
The wades print looks like your extruder isn't properly calibrated, have you printed a thin walled box and verified your extrusion width?

wades: Too high or too low? And what shows that? Non-water tight filling of the surface?

I'd guess too low, The fill on the top layer is too sparse, but I'd print a single walled test and compare the measured wall thickness to the expected wall thickness.