Engines gerenally shouldn't burn oil. Could well be valve stem oil seals as it is obviously slowly 'seeping' in to the combustion chamber overnight - then quickly being burnt off.
I wouldn't do anything unless it is using masses of oil, it simply isn't economical to do so. Lots of cars smoke a little on start up and I am sure there is no performance issue (unless it is really bad), just a bit embarassing if you cover passers by in smoke!
I have had loads of old cars that do this, its when it smokes when it is hot that the engine is getting really tired. Having the work done (£Â£Ã‚£Ã‚£Ã‚£) save you from a bigger bill in the future.