You do not need BES. That is usually for corporate users and their company has a BES installed with their corporate email servers. You can subscribe to a 3rd party hosted BES provider but it's another monthly fee.

If you are just wanting to get rid of the GMail sent mail issue, simply log into my.t-mobile and go to "setup internet email." You should see your gmail account in there. On the right are links for "edit", "filter", and "delete." Click on the one that says filter and set up the filters as described above. You want to not forward to handheld all mail that comes from your email address....