There are a number of official lists of kanji. I’m not an expert by any means, I’m just going by information gleamed off the net.
- 教育漢字(kyouiku kanji): The 1oo6 characters students must learn by grade 6. Essentially, knowing these characters is a good start, but you’re far from finished.
- 当用漢字(touyou kanji): A list of 1850 characters published first in 1946 approved for use in public documents and the media. Many characters that were in use until then were simplified; for example, 學 became 学.
- 常用漢字(jouyou kanji): Last updated in 1981 and the successor of touyou kanji, 1945 characters that basically you ought to know as a literate adult. Used in legal and public documents, newspapers, magazines and broadcast media.
- 新聞漢字表(shimbun kanji hyou): A standard agreed upon among newspapers based on jouyou kanji, but removing some characters and adding others. The link is to a Japanese Wikipedia article, but the explanation and outline that appears there is possibly under copyright and could be deleted from the site in the future.
- 人名用漢字(jin meiyou kanji): Characters approved for use in people’s names. As of 2004, when the government had a heck of a time trying to update the list, there are 983 extra characters than can be used in addition to what’s already in the jouyou kanji list, or that are variants of jouyou characters, and most of them are really, really hard to read. The only way I’ll ever learn them is if I get a chip implanted in my brain someday.
Incidentally, mainland China also simplified their characters sometime after WWII but for obvious reasons they didn’t give a rat’s ass about how Japan went about doing the same thing, so in many cases the two countries simplified the same characters but in different ways.
Summing up, if you’re pretty smart, my guess is that you know around 3,000 characters or more. Multiply that number by a few factors to approximate how many readings you’d need to know for all those characters.
As for me, when reading a novel in Japanese I have to look up an average of five characters per page, and I can get through around 15 pages in 2-3 hours when I’m reading to learn. It’s tedious, frustrating, labor intensive, tiring, and makes me feel learning disabled, which is why I avoided serious studying for far too many years.