I'd begin by taking her out to sight in and fire at least a couple of groups from a good rest as a benchmark of accuracy.
The NM op rod spring guide would be a good first bet, and a new rear sight setup might be a good idea if you find the Norinco sights wanting.
I'd get a good mount for the optics (i.e. CASM, Pro Mag, ARMs 18 or decent scout mount) and a scope of your choice. For reasonably priced options I'd look out for a Bushnell 3200 10X target scope or a Bushnell TRS red dot.
I'm not yet up to speed to comment on the TIG welding, shimming of the gas system or smoothing up the trigger group, but those are relatively inexpensive mods that you could do over time as you see fit, making full use of the knowledge available on this site or one of the ongoing M14 clinics. The rifle could probably still provide loads of fun and decent accuracy in the meantime.