Automatically move mail from Inbox to folder and delete from Inbox

I've never really used the bundled Mail app but I've decided to give it a go and I can not find or figure out how to set up a folder with rules like in Outlook.

Basically I like to have folders/mailboxes that collect messages based on whatever rules I want and incoming messages get moved to that folder/mailbox and never appear in the generic inbox for that IMAP/POP account.

I've played around with the smart mailbox but they leave the original message in that account's mailbox. Is this possible to accomplish in the Mail app?

The only way I can think to organize in this manner is to create a generic inbox that filters all the mail from all my other folders/mailboxes so I can see mail that does not fit the criteria of other folders/mailboxes. Which seems redundant and then I still have a million emails in the default Inbox.