I wouldn't recommend doing it for mc. They keep changing and or using old jvms. What I do is I just go on oracles site and get the jdk they list that works, and run it directly from the folder. Also some distros do make it a pain lol.
I haven't done this in forever, but last time the recommended OpenJDK answer was somehow not right. Got the Oracle one, had to figure out where you extract the tarball to, fix my
PATH, yada yada.
That sounds fine though. The PATH variable is a nicety for the user to not need to type long paths, really like using ~ for the home directory, not for program setup.