Welcome to TRS
White smoke at start up is normal and depends on outside temperature
Any time you burn gasoline(a Hydrocarbon) with Oxygen you get H2O(water) as a by-product
This is why water drips from tail pipes and exhaust systems rust from the inside out
If the air going IN to the engine is also humid then there is even more water vapor in the exhaust
When you shut off the engine exhaust flow stops, and exhaust starts to cool down, any water vapor will condense inside the pipes, Cats, and muffler, and the rusting starts, lol
But this water vapor, now pools of liquid water, just stays there
On the next start up the exhaust system heats back up and along with the "normal" water vapor you have the "extra water" vapor from the liquid water that's being vaporized by the heat
This extra vapor is not as hot as the by-product vapor so tends to condense quickly after leaving the tail pipe so "white smoke" until its gone
When outside air is very cold ALL gasoline engines have white smoke coming out the tail pipe all the time, the cold DRY air condense it very fast
The other non-white smoke is from worn valve guide seals most likely, fairly common on older engines
Oil in the valve train is SUCKED into cylinders by intake vacuum via the intake valve's stem, there is a rubber seal on the stem to prevent this but they get old and crack
This "smoke" is even more noticeable after deceleration and then acceleration because when decelerating engine vacuum goes high, +30" maybe, that sucks in ALOT of oil, which is then burned when accelerating and seen as the puffs of smoke
I would change PCV valve and make sure its hose is clean, PCV valve puts negative pressure in valve cover which helps to prevent valve cover gasket leaks AND less oil going down valve stems
Its possible worn piston rings are to blame, same symptom
But a compression test can tell you which it is
Worn rings effect compression, worn valve guide seals do not