If you spend a chunk of your morning and afternoons going through a bunch of inbox items only to just delete or archive them, learn this one thing: keyboard shortcuts.
If you use webmail (which you should, it's faster than most email applications, if not all of them), first activate keyboard shortcuts
Google includes more instructions on how to do this here:
There are all sorts of shortcuts but the most important ones to learn first are
J and K (for up and down)
X (for selecting)
E (for archiving)
That's it to start: just practice going through your inbox moving from message to message, mark the ones you want to remove from your inbox and then just press E to archive them.
It's extremely fast and with the tremendous amount of included storage there's just no benefit in deleting messages any more - archive them so you can easily search for them later. You never know when you may need an otherwise-deleted message in the future.