I have never changed store (or anything else of importance) a constructor, and I have played quite a few games (but not for ages). I think you will find that the default designs work quite well.
I think (but am not sure) that they pick up what they need for the job, and they manage to build mines, resort bases, and whatnot without much issues. Sometimes they get stuck, though, and I seem to remember this is more common when repairing derelict ships. Problems of this sort are probably more due to lack of supplies, than lacking storage space.
If you ever notice a stuck constructor, typically with lacking materials in inventory, you can try to send it away (just any order), and then order it to repair what it was building. It should then head to a space port, pick up materials, and finish the build.