Archiving Gmail messages in Apple Mail

I use Apple Mail to manage my Gmail accounts, and my inboxes have become very messy. I don’t have time to sort through them right now, but I’m sick of looking at my current message number and want to see Inbox Zero again.

If I select all the messages from my Gmail accounts and archive them (using Apple Mail), how will this affect how I see them if I were to log directly into Gmail.com itself? Is it better to archive directly using Gmail? I hesitate to do this, because Apple Mail is my primary email app and I want to be able to search and find my archived messages easily if I need to retrieve one of them.