Blueish gray smoke from exhaust

If you only see the smoke on the first start it is likely to be from valve stem seals that have hardened or cracked. That lets oil into the cylinder as the engine cools down and the contracting air creates a vacuum in the cylinder and pulls it through the worn seals. Then when you start the car the oil burns off and the cylinder pressure keeps most of the oil out. Repairing it would mean replacing those seals. That is when it gets expensive. Book time is 12+ hours because most of the top of the engine has to come apart to do the repair and with the mileage you have the rings and other parts are worn as well. Replacing the entire engine is about 2 hours more in labor plus the price can be $3,000.00 to $4,000.00 for a re-manufactured engine. The choice is going to depend on the condition of the rest of the car. If it has no rust or other problems then it may be worth the repair or replacement. Then you may want to look at the cost of a complete replacement vehicle against those options as well.