Baal Teshuva with a Non Jewish father?

I am a 14 Year old who has decided to become more religious I dont think its necessary to say why for this post. I have been accepted to a pluralistic day school which I view as a good stepping point to higher observance due to the fact it has an orthodox minyan, hebrew, and limudei qodesh. My Father isnt Jewish most likely their are some family rumors about his mother being adopted from a jewish family but thats unlikely. My Mother is a Ashkenazi jew. Would him not being Jewish effect my chances of getting into Yeshivas and hurt my shidduch chances as well as general integration into the frum community. Obviously my school is very welcoming so I dont have a good idea of what the wider community is like.

Thank you in advance