"myśleć" is literally "thinking", so every time you would use "I think that[…]" in English, you would use "Myślę, że[…]" in Polish.
"uważać" is pretty close to consider, other popular "opinion indicators" in Polish are "Moim zdaniem" - "In my opinion", "sądzić" - literally "judging" but also used to state opinion("Sądzisz, że on jest dobry?") and quite a few of others less popular(I think).
The point is that the adjective "dobry" indicates masculine gender,
so "on" is redundant and may be omitted. The other thing is that
"on", even if implied, can refer not only to a male (he) but also to
a masculine noun, eg. "dobry nauczyciel/dobry pies/ dobry film/ dobry krok/dobry dowcip/dobry kierunek/dobry obiad" (a good teacher/dog/movie/step/joke/direction/dinner, respectively).
Different ways of conveying the same message.
"Do you consider that he is good?" works as well, with "he" being a very direct equivalent of "on".
Polish, as you know, has a lot of cases, English almost doesn't, but he->him is a reminiscence of the times when it had cases as well. But usually you won't find such situations with different English cases, so nothing will make you wonder about it. I understand that it's a little confusing here, but both versions in English are correct, both versions in Polish are correct, it's just the matter of which one is a bit more natural and probable in usage.
But would it really mean that it's your opinion? Or rather that you are right now thinking and wondering about whether he is in fact a good person? Same with your other comment, "Have you considered" - that won't work because of a wrong tense, but anyway, doesn't it also mean "Have you given it a thought that maybe he's a good person"? The Polish sentence asks about your opinion.