Hopefully, someone else will post here. I am not a Catholic Priest. You will need to be a practicing Catholic for a couple of years before you become a priest. This is logical due to the fact that you would be a recent convert. Mid Thirties is not too old. There are much older Seminarians (in fact there is a link here for a seminary specializing in second vocations).
If you want to belong to an order (eg Carmelites, Benedictines) you will likely have a bit better luck being under 40.
What would I do?
i) Let my Priest know.
ii) Set up an appointment with my Bishop if I intended to be a diocesan priest. Get his guidance on the path to follow.
iii) If I intended to belong to an order start exploring and making contact with the order. Become associated.
iv) If you do not have you undergraduate degree begin working on it. Philosophy is a good major but there are others.
v) Start looking at seminaries.
When you are ready to start you will be ready. Building relationships is a good idea rather than showing up out of the clear blue in a couple of years. You are going to want to demonstrate a life that is devout and studious in terms of your faith. Also well rounded (i.e. stay active). It was so cool to see the picture of the Carmelite kayaking. Being a Priest does not mean (necessarily) sitting on a stone bench chanting. Jesus was dynamic and met people where they were. Watch out for temptations to sin but enjoy the life God has given you as a witness to your faith.
God’s blessing upon you!