Just set it up as a normal BIS account. You can have up to 10 email addresses on your BIS account with TMo. You are already paying for it.
It will be push email just like any other on your BB. I read in your first statement that you didn't want push for whatever reason. But that is what you need.
Here: How to add / delete email addresses - BlackBerryFAQ
I'm not figuring you should webmail, that would be a royal pain. Just do it the normal way, to your Messages folder.