h3 is absolutly a better solution than h2, h1 or h6 !
You have to use specific level : if you're in a h1, use h2, if you're in a h5, use h6 (if you're in a h6... hum, use strong or em for exemple). It not a obligation but a question of accessibility (Here, green part).
You don't have to give title to list... because this element it doesn't exist. So screen reader will not use something special.
Therefore, using Hn is probably one of the best solution, but surely not a specific level.