Armour and weapons can be found in chests as you complete through the story missions, or at the merchants of each town.
The merchants will change their stock once in a while, so be sure to check back. If you are unable to find the equipment you want at the merchant, you can try again when they restock.
Below is an example of equipment sold at the merchant. The time indicated in the picture is when the merchant will restock their wares.
If the timer is stuck, simply refer to this article: Frozen Time.
If the refresh timer is greyed out, please refer to this article: Disabled/Greyed Out Refresh Button.