Is the best way to achieve this to offer three radio buttons on the checkout page and then have the Shipping rules, in the Shipping tab, respond to which sessions are made live by the users selection from the radio buttons? 
Yes, add the 3 radio buttons to the checkout page, using values like 1 for first class, 2 for standard and 3 for next day.
then create a shipping rule for each shipping type and weight / price range option.
for example, if the session is named shipType:
First Class
Under £75 + under 1kg = £3
triggers:
based on Session variable Value "shipType" has a value of "1"
and
Based On column subtotal "weight" is "<" "1"
AND based on cart subtotal "<" "75"
