How would you say, "what would you like to have read?". As in, what book do you wish you could have read at some point in your past? Because that is what i though this sentence was asking.
Either the same, or more clearly "Co chciałbyś był przeczytać" (with an additional 'był'), but that's plusquamperfect and isn't really used anymore.
Your interpretation is correct linguistically (added), although as you noticed, rather surprising. The Polish sentence is almost certainly a normal conditional sentence, 'what would you like to read tonight'.