Does it make sense to start with the movies?

If you want to go full on the Universal Century (UC) timeline, go for it.

But they are from the 70s, so don't expect top notch animation and scripts (it's a product of its time).

After that you can go Char's Counterattack and Gundam The Origin (this is a recent series, so more polished animation). Later maybe try watching Zeta.

As another comment mentioned you also some shorter UC side-stories like War in the Pocket, The 08th MS Team and Stardust Memory.