If I change civilizations, will I still have my progress from my first civilization?

Yes, your progress and everything else would be the same, this includes your commanders, buildings, troop count, technology and more.

The only thing that would change is your city style and special civilisation troops (for T4,T5).

Troop numbers would still be the same. Your starting commander will also not change, meaning for some sculpture exchanges event you will still be exchanging for your starting commander sculptures.