"책을 읽고 의자에 앉았어요"
would be the best fit.
Korean is very ambiguous when it comes to "prepositions", but it makes it up with the plethora of verbs.
앉다 is "to sit" exclusively for "to sit on a seat/suitable spot" for a lifeform.
And a chair is a chair, a spot to sit on.
Therefore, we don't say "의자 위에" but "의자에"
The universal ~에 "preposition" is godsend, jus like "~하다" for so many verbs.
You can consider "~에" to be just a particle indicating that the noun is a "dative object". (Maybe it actually is)
Don't bother much about the prepositions. Focus on the variety of the verbs instead.