Catalyst and Inhibitors home experiments
You might look up the decomposition of hydrogen peroxide, $\ce{H2O2}$. The 3% solution sold as antiseptic should be safe to use at home, as would be some readily available catalysts and inhibitors.
Horseradish might be used for a catalyst... but don't eat it in the lab.
To measure speed of reaction, measure gas evolution with an inverted, liquid-filled graduated cylinder or small measuring cup over time.
You can have fun burning things (carefully) in the evolved $\ce{O2}$, too.