Hi Mike!
If you have to rebuild your engine on a budget, and wear in the cylinders isn't excessive, you might get away with new rings. But in any case re-hone the cylinder to allow the new rings to bed in properly, as Trev said!
Damage to the new rings by a (not too bad!) ridge can be prevented by fitting a thicker (or two standard) cylinder base gasket(s).
Beside checking piston to bore clearance (10 thou is absolutely rebore-time I'd say), it is also worth checking the piston ring end gap in the larger bores. Rings of the next oversize can be modified (shortened) to give proper end gaps (and thus sealing) despite the larger piston clearance.
But don't expect top notch performance, you'll rather encounter some piston slap when cold and increased blow-by and oil consumption probably, but you should get a few more miles out of the engine that way.
Cheers, Markus