Smokes really bad at the beginning, but after you drive the car for 15 min or so it almost stops. What could that be?

Hi :) What is happening? you say Well when you shut the engine down the oil is hot and it runs by the valve stems because the stem guides are warren out and sits on the piston till you start the engine next time. It take a bit to burn it off then it burns clean till the next time you stop running the engine for any lenght of time.Take it in to the shop and have new valve guides put in it or unbrella seals put on under the valve spring this will stop the oil from leaking past the valve stems. I put a cup of transmission oil/Fluid/Dexron2/3 every time i change my oil to keep my valve seals soft and rubbery and it helps

Blue smoke is oil burning, and it could be that when the motor warms up the piston rings are expanding and sealing up. Black smoke is to much fuel and needs a tune up to fix. White smoke is water burning and could be water in the fuel or a blown head gasket leaking antifreeze into the motor. If it's burning antifreeze, the smoke will have a sweet smell. I would start with water remover in the gas tank.

When the smoke is white in color when it comes to oil smoke, this may come of it if the degree of engine wear is too large or if the Cylinder head gasket is broken somewhere.
When the smoke is unburned fuel, is a bluish hue.
When it comes to the unburned fuel in this case is heating up too much or not splashed sprayed it properly. This may be the cause.
Specifically, your car is probably one of the injector is not working properly and this leads to a cold engine smoke.