It is important to be systematic and record your results as you go. What information will you need to record for each simulation so that you can decide what factors affect the probability of $H_0$ being rejected?
It makes sense to change one factor at a time when exploring how different factors do or don't affect the probability of $H_0$ being rejected.
How many times will you run the experiment before recording the proportion of times that $H_0$ was rejected? Do you need to decide this before you start?