So, I personally read a lot of anime fanfic (people use honorifics sometimes in dialogue) and that's how I learned, but the basic ones, aka the three you mentioned, are pretty simple.
San I think of as like Miss/Mister or something along those lines. It's the default, I think.
Chan is informal for girls, so like girls you know or maybe also girls you're higher up than? Not entirely sure about that last part.
Kun is kinda like Chan for dudes I think, informal for boys.
The main other one I know would be Sensei I guess? It can be used as an honorific to my knowledge, though it just means teacher.
Hopefully I helped at least a bit, I wish you luck in your Japanese! (Also hope I got this right, I'm not 100% sure because I learnt from fanfic.)
Sensei is not just for teachers, but also doctors, lawyers, and such.
Another common one is sama. You probably won't use it yourself, unless you deal with customers/clients, but you will be addressed as such quite often. For example, when the doctor calls you into the consultation room, they will say so-and-so-sama.
Be careful with kun/chan. It can be very patronizing if used improperly.
And don't refer to yourself with any of them, just your name.
Just to clarify, as far as I know, ちゃん is for 'familiar people' and not just girls. You can call your uncle or grandparents -ちゃん, like おじちゃん or おじいちゃん / おばあちゃん. It leans more towards girls though (usage note on ちゃん )
