You have the option of using an external Mail application for GMail. I recommend Thunderbird by the Mozilla folks. It’s really well made, runs with fewer resources than anything that Apple or Microsoft makes, and has better features which integrate with the Web, making it more than just a mail application.
OK, off my soapbox for Thunderbird now.
To do this, click the Settings link in your GMail page (upper right-hand corner of the window).
In the Settings page, look at the top for the Forwarding and POP/IMAP link and click that.
Go down to the third section and Enable IMAP.
Then click the Configuration instructions link to complete the setup.
POP is nice, but it tends to do weird things, like put your sent items in the Inbox for your e-mail application, which is really annoying and I believe the type of thing you are attempting to avoid here.
Now you can manage your mail as you wish; create folders, subfolders, categories, filters…whatever you want!