What Belthazar said; additionally, though, as someone who learns best through patterns, it was useful to figure out that 「がつ」is normally used for specific months (四月、五月, etc), whereas 「げつ」is more for talking about months in general (先月、来月, etc).
As for 人, it’s definitely a lot more erratic but from the relatively low amount of vocab I’ve seen it seems like 「にん」is more common when the term starts with 人 whereas 「じん」is usually the reading the rest of the time. (Again, though, not a hard rule by any means.)
Also obviously I’m the same level as you so I’m not the most experienced, I just thought I might be able to help anyways.