Kempe, unless your engine has been butchered in some way by a previous owner, it should be easily fixable. Briggs engines are notably reluctant to quit, and easy to repair.
Just begin by testing the spark. Remove the spark plug, re-attach the high tension lead to the top of the plug after removal, and hold the metal body of the plug against a bare metal part of the mower (usually the cylinder head). With the speed control in the start position, pull the starter briskly, watching for a series of blue sparks across the contacts at the opposite end of the plug from the high tension lead. If there are sparks, the problem is not ignition. If there are no sparks, tell us and we'll talk about next steps.
The only thing likely to threaten the viability of your engine is the exhaust smoke you spoke of, not trivial stuff like failure to start. The trivial stuff we can sort out in a flash.
