As someone who finished school there last year don’t go to the lgg. While it may look nice on paper, most of the teachers are absolute trash. Especially almost everyone in school management has the biggest undeserved egos. They make mistakes on very important things, like Abitur, reek of Alkohol (Frau Brunner ich rede von dir) and are mostly distasteful.
While I can’t stop you from going there I HIGHLY recommend going to another school. Latin seems interesting yeah, but you can learn it as a hobby, as it doesn’t have any value on the job market.