My experience with hard starting engines is due to old gas in the carborator from being stored off-season. I dissemble the carborator (paying attention to the needle valve settings), give it a good cleaning, put it back together and fire it up. When the engine warms up I fine tune the needle valve settings.
For the tecumseh engines that I own (8HP snowblower and 3HP edger) I installed fuel shut-off valves between the carborator and fuel tank. When I am done with the snowblower or edger, I shut the fuel valve off and let the engine run until it runs out of fuel (from the carborator).
Another area you might check is the spark plug. If it is carboned up you might have to pull the head and clean off the carbon. If the plug is wet you are flooding the engine. If the plug is dry you are not getting enough fuel.
1998 Mercedes E320, 200K Miles
2001 Acura 3.2TL, 178K Miles
1992 Chevy Astro, 205K Miles