From (my) consumer point-of-view, the "fairest" way would be to either not select an option, or – if that is not possible/desirable – to select the cheapest/free option. The main reason being that the cost (to the customer) of "premium" shipping options is almost certainly at least as much as the cost to the seller, so pre-selecting a premium option will (slightly) increase profits and may make your website appear to be "money grabbing".
Beyond that, if you have "memory" of previous visits (either through agreed-to cookies, or settings in a customer's account), you could:
The first time they are presented with the choice, add a "Use this as my preferred shipping method" checkbox.
On return visits, if they ticked that box, pre-select whatever was their preferred choice of shipping method.
If a returning customer changes from their preferred choice, re-display the "Use this as..." checkbox (unchecked), allowing them to choose between a "one-off" change (e.g. for an urgent item), or an ongoing change of preference.