Try a squirt of Starting Fluid .. if it jumps to life without fail, the carb has a problem delivering adequate fuel when starting.
If it's hard starting with the choke on or even when the engine is warmed up, the carburetor needs attention.
The next step would be to clean and adjust the carb.. check the whole fuel system. Air and fuel must flow freely without leaks, without restrictions anywhere.
A low float level can cause inadequate fuel delivery while starting and when accelerating from a stop. Float level actually affects things at all speeds, but low-speed, low RPM troubles are more noticable.
There may be other symptoms you've not mentioned that would indicate the engine is actually flooding .. perhaps float level is way too high.. Anyway, no popint in guessing about it. Give it a thorough tuneup and examination. A couple hours spent cleaning, tuning and tightening things will clear it up.
"FREDs GUIDE":http://www.mopedriders.org/article_view.php?faq=2&fldAuto=8 will .. errr.. guide you.