There are around 2000 kanji that adults are expected to know by the time they finish school. The schedules on Renshuu will start with the most common ones, ones kids also learn first, but it's not like I can just list a handful for you and you'll be set. Learning kanji is a long journey.
Readings have to be inferred from context. Learn the words kanji are used in, and then you can recognize those words.
It might depend on your tastes in entertainment, but the anime that I watch tend to feature a lot of obscure kanji. They’re either associated with ancient Chinese mythology or the occult.
