So i'm looking to buy my first non box store bike but i'm wondering what sort of bike I should purchase, My goal is weight loss and cardio for my workout regime so I ride on the road with lots of hills, would I be best off with a road bike which I'd travel faster on or a heavier but slower bike like a mountain bike. Would I get the better workout on a road bike or mountain bike given distances and terrain is the same.

max of 500$ or so is my budget, college student