If you are not good at climbing, you may visit Mutianyu Great Wall(https://www.travelchinaguide.com/china_great_wall/scene/beijing/mutianyu.htm) which is relatively gentle. If you plan to do some training for climbing the Great Wall, I think one month is enough.
By the Way, most of the great wall sections are renovated well and built with gentle steps at most places, it's not so hard to climb as what you are thinking of. Anyway, good preparation is necessary.