Well, it's obvious you didn't write these classes. I say that because your code is mildly complex, but your question is pretty basic. You should pay me for going through them J/K 😃
You will need to query your users table again with the credentials that were set to properties already (as checkuser returns true or false only.) The appropriate place seems to be in the set_user() function as you have indicated. Just query the database in there for the "userpage" data that I can only assume is a part of the $this->table table.
Your query will look something like this:
$sql = sprintf("SELECT `userpage` FROM %s WHERE BINARY login = '%s' AND pw = '%s' AND active = 'y'", $this->table_name, $this->user, $this->pass);
All you have to do is set that result to your session variable and then redirect appropriately.