Yea i agree with Bill, r u sure its rings? not alot of times u just change the rings, I would also do the bearings etc. while ur down there. For instance in my school, we got a car that came in saying needs rebuild, burning tons of oil, so we change the rings, bearings, gaskets, valve job etc. and we found out the original problem was from the tube from the crackcase to the intake(cavalier) or something like that and the tube was crimped, that was what caused the oil consumption.
I would do a compression (wet and dry) and leakdown test and go from there, they will tell u alot Good Luck