Do you have any parts at all? i.e. dvd drive, copy of Windows, keyboard, mouse, monitor?
If you are starting totally from scratch, I don't think $350 would cover it.
I have an old PC in storage a few years old nothing special it's an old family computer and i could probably salvage some parts of that.
A copy of Windows is $99. That doesn't leave much for the other parts, plus monitors are usually around $120, depending on the size. I would wait and continue saving, maybe start when closer to $500 or $600.