Moisture in your exhaust was condensation almost defintely. If it were coolant you would have had a lot more than a puff of steam.

If you are seeing oil in your coolant though then yeah, you likely have a head gasket or head issue.

 

Your symptoms of initial rough start up and then improvement once engine up to temp is consistent with a blown head gasket. There can be a small breach in gasket over one of the cylinders just enough for some coolant to enter the combustion chamber and cause the misfiring/rough idle, then after engine heats up enough it can expand and seal up the breach in the gasket enough while also burning off the coolant in combustion chamber that leaked in over the time between running the car. This kind of head gasket failure is most consistent with corrosion/not keeping up on flushing coolant often enough. The fact you saw oil in the coolant is also reconfirming give away.

Depending on how long this has been going on/how long been driving this way, the coolant can compromise the cylinder wall and rings, so once head is off, do a good inspection and make sure the cylinder walls are ok to slap another hg on and be good. You might have to pull the one or several pistons and do a light brush hone and new rings on old pistons just to insure the rings seat properly again with proper cylinder cross hatching if the coolant compromised the cylinder walls. You can leave the crank in place and just pull the pistons from top of motor and protect everything down bellow from any honing material. This assuming just one or two cylinders that got compromised.