ideas for creating linear movement/ general suggestions for approach please

lax123:
Does it work the way i imagine it?

In an ideal world, yes. But what happens if the stepper misses one or more steps (or oversteps)? Then where the Arduino thinks the syringe plunger is at versus where the plunger -really- is at are two different things. Thus the need for some sort of feedback mechanism (a linear-taper, linear-slide potentiometer could work in this manner, for instance). You would want at a minimum limit switches at each end, so that if for some reason there is a problem or error, you don't over-travel in either direction - which could break the mechanism, motor, drive electronics, etc (if you didn't want switches, you might try monitoring motor current instead - though that is more complex, especially with a stepper, depending on your driver electronics).