I use a mineral sunscreen (Australian gold tinted) with the regimen, no issues with it and no breakouts!

I use Missha Gel SPF and Innisfree Mild Sunscreen and apply with air puffs. For some reason, any sunscreen I apply with my hands makes me turn bright red but since I started using the air puffs to apply, no more irritation. Take a look at websites like stylevana.com or yesstyle.com. They sell many korean and japanese sunscreens that do a great job of protecting your skin and don't have the dreaded white cast.