There are no "budget conscious" options. If you re-ring it and the valves need grinding you have not accomplished anything but depleting your checkbook. If you re-ring it and do a valve job then you will still have oil pressure problems due to wear. Maybe you could find another engine that might be better.
Rings, pistons, main bearings, cam bearings, rod bearings, valves, etc. Add in machine work and labor to pull the engine, rebuild the engine and reinstall the engine. Buy yourself an engine manual for that engine and shop it around. I'd be amazed if it came under $5,000.
There is absolutely no sense in partially rebuilding the engine, in my opinion.