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"