Hey there little missy!
I'm glad you decided to venture into what's called 'aesthetics' and 'style', but you picked a real doozy to start with! Some people are ok with violence and gore, so long as it's done in a stylistically interesting and pleasing way, and Primal fits that bill pretty well.
Primal is also a good example of a story that can be watched on multiple levels. It can be about grief, partnership, the balance of intelligence and power or even friendship depending on how deep you want to go. Why, half the fun of this show is just sitting there and thinking about it. But, if you just want to see a man and a dinosaur fighting things it'll scratch that itch also. Believe it or not, a lot of men like seeing violence and themes at the same time (for examples, see the Conan books, Moby-Dick or The Lord of the Rings).
Anyways, I'm so glad you decided to start your journey into appreciating animation, but I'd recommend starting with something lighter, called 'The Secret of Kells'. It's even got a girl in it, so I'm sure you'll enjoy it for that if you can't get into the gorgeous animation or storytelling the first time around. >pic related
Here's a little preview to give you an idea of what you're getting into>https://www.youtube.com/watch?v=7VT3ewiaMys
Don't be afraid to post here if you have any questions about it!