How vigilant do I need to be about foods with fewer than 1g of carbs?

Hey people, I am going to Costco this weekend to stock up and will be starting keto. I've been planning some meals it in advance to be under 20g carbs. I've been reading countless reddit posts and come across info regarding products which say 0g carbs can be rounding down due to packaging laws. For instance, I've read that while an egg says 0g carbs, it actually contains .4g carbs. I have read the same about different types of cheeses. Do I need to do more in depth research for my macros, or are these carbs not enough to worry about? I have two eggs with my breakfast each day.

Also, do you guys have any go to sites for looking up nutrition info? I am considering having a small amount of strawberries with breakfast, but finding that google and multiple different websites (not brand specific) give different info for carbs and fiber in strawberries.