Well starting off in a symmetrical form is the only way to go anyways if you don't want the parts to attract each other, messing up the orbit in the first place. Secondly, can't really suck out metals out of stars as they don't produce them until they're at their end of their life. By the time the star's core is made up of helium it expands into a red giant, which could be a real problem for your ring world, for obvious reasons. And the amount of materials needed for a ring world is . . . extensive to say the least. You may want to use fusion to acquire those materials, but there are two problems with that. Energy. Fusing hydrogen materials on a small scale (without the assistance of star levels of gravity takes a lot of energy). 

Smashing particles into each other to create measly amounts anti-matter also takes energy. You can't create energy/matter out of nothing.

Using the 4 starting points to supply the solar power needed for fusion and the anti-matter bit would doubtfully be enough to provide the required energy. At that rate it take . . . well a lot of time to build it.

Also I'm still not quite sure where the anti-matter comes into play. That has to do with the ring-world itself, anyways. Of course anti-matter has a lot of applications. Weapons, Engines for ships, etc.