Express? You're going to lose a lot of sales. No one in their right mind is going to pay more for shipping than the cost of the shirt/cap.Since I am just selling shirts and hats right now, I plan to limit orders to USPS express shipping with small and medium box to keep it simple.
Suggest you rethink and look into first class for weights a pound or less and priority for heavier.
As to the software, it's only as good as the info you put into it. It will calculate any shipping method you want accurately as long as your weights are accurate. That means weighing every product/every size that you will be selling.