Generally, smoke at start up is usually related to oil running down the valve stems. If it was black smoke I would say the carb is running a little rich. If you are seeing smoke under the hood, that is likely from oil leaks. Most likely that would be valve cover gaskets.

As far as A/C, need more info. Are all of the pieces there? IS the system charged? Is the belt on the compressor?

Scott

i agree with ranger, it is most likely a fluid dripping on your exhaust in your engine compartment, it will take a few minutes for the fluid to burn off the exhaust pipes. check your mainfolds and exhaust below the firewall, and looks for stains, if oil is dripping on hot exhaust, it will leave stains. if this is the case i would reccomend getting it fixed since oil is flammable and can ignite, hate to see your vette burn up. next time it smokes open the hood and try and see where it is smoking from

I agree.  But the black deposits in your tailpipes are either soot or oil.  If they are very oily, you have an oil consumption problem.. If dry and sooty, you are just running too rich.

Larry