1/ it will only ever be as good as the pivots.
2/ triangulation of the "muscles" to as near as possible equilateral triangles when in the centre of the movement envelope.
When you get it built avoid rapid / sudden start / stops, that makes it sway and you have to wait for that to damp before you get your positional accuracy, and of course the more weight you carry the more the swaying...
acrylic adhesive / solvent, essential, 3 x 10 mm thick base pieces all flex, welded into one 30 mm thick piece it is surprisingly rigid even before you add the flanges.
The linear stepper motors are available (in the uk) from
http://www.motioncontrolproducts.co.uk/ as "captive linear stepper" priced at £7.89 each (I do not work for or have any interest in MCP etc) if you want to go that route to making the "grab"
the stiffening between the sides is essential, once you get the muscles sorted and positioned, you turn two parallel flat bars into box section that way.
really, really, really don't be going for fast motion with these, the slower you can run them the more accurate they are.
AT the low end acrylic is wonderful stuff, you can drill and tap it, which means a bog standard coupler like the old meccano shaft coupling (small brass tube with two grub screws to clamp shaft ends inserted into tube) can be used to attach a bog standard leadscrew / threaded bar to the stepper, and the other end you can just drill and tap a block of acrylic to suit the threaded bar.
Sure it is going to be a bit flaky and wear out this way, but it allows you to experiment on the cheap, quickly, and that is what this project is all about, above all else, it is a robot arm experiment / development kit project.
If you pull 3 connected bits out of the design and use them for something completely different then it has served its purpose.
As usual it is a deliberate study is doing as much engineering as possible with minimal levels of materials complexity and cost.
Worst case scenario is you got through 25 quids worth of acrylic, modified it slightly, and ended up with a toy crane for a boy.