Although creating and saving your edits to an overide file is the best way (no pun intended); if you are not really worried about the consequences you will face later while upgrading, (or somehow you already have that covered), then this is a quick and easy way of changing the "Best Way" text:

You will need to edit the following files:

includes / languages / english / modules / shipping / item.php

AND

includes / languages / english / modules / shipping / perweightunit.php

of course, this is assuming you are using English for the language (you get the idea though)

Open these files in your text editor and you will see something like this:

(for the Per Item)
define('MODULE_SHIPPING_ITEM_TEXT_WAY', 'Best Way');

(for Per Unit)
define('MODULE_SHIPPING_PERWEIGHTUNIT_TEXT_WAY', 'Best Way');

These should be the last lines in the (really small) .php files.

Now just change the text 'Best Way' to whatever your heart desires. Ensure that you leave the ' ' around your new text. So it could be changed to something like:

define('MODULE_SHIPPING_PERWEIGHTUNIT_TEXT_WAY', 'We define carrier');

Again, this is not the recommended way of changing this, but here is the info anyways. Hope this helps!