Need Help Please ASAP

Hey guys it’s been a while since I posted last, since the last time I posted I have gotten my 91 LS-S running but I have noticed a couple things that concern me, one of the issues is that at idle it seems to be smoking, the smoke is a white/grayish color, the second which has me severely concerned is that under medium to heavy acceleration it smokes(white) like a damn diesel, my question is that with the the smoke I bought a new head, should that fix it or should I re-ring the engine while I have the head off? A little background on the car, I bought it for $600 as a no crank, no start, was given some lame ass excuse as to it was running and just died, well I bought it, took it home and pulled the valve cover, timing belt was intact, pulled spark plugs and the head of one was chewed off, pulled head and the piston was gone with the rod wrapped around the crank, bought a block, then set the bare block aside and found a whole b18a1, pulled the head, inspected it, and bought the engine, got it home put new gaskets and bearings in it, however I never replaced the rings, put the old head back on correctly, timed it, dropped in the engine and trans, fired it up after a couple small issues, after it came up to operating temp i noticed it smoking out of the exhaust, didn’t think anything of it, took it for a test drive and noticed it blowing white smoke, turned around and parked it, I was told the valve stem seals were bad and that I should just get a new head, well I did that but I’m looking for advice to see if I should replace the rings before I put the head back on. TYIA

head gaskets dead.

check the coolant too see if its milky like oil got in, next you could pull spark plugs and look inside for water and lastly you could do a compression test

but white smoke is a head gasket

didnt get the head decked did you?

No I did not, I just tossed the old head back on, and didn’t think about that, I went and bought a new head instead of trying to figure it out, the anti freeze looks good and so does the oil, I made it maybe a half mile from my house when I noticed it smoking