There's probably no special basic set of hanja that new Korean learners are supposed to learn. It's even debatable whether hanja is necessary at all, although most people agree it is helpful.
Traditionally, there are 900 hanja characters for the middle school (중학교 교육 한자 900자) and another 900 for the high school (고등학교 교육 한자 900자) . These are the standard hanja characters all Koreans were supposed to know in the old days when hanja was more active in the language. They are not officially taught anymore (still most people in high profession have good command of them), but anyone who wants to know hanja can start with the first 900 characters.
This Wikipedia page has a link to the list of all 1800 basic Korean hanja characters: