Hi,
You should not set the shipping price in your products in that case. Instead, set the weight in them.
Then, create manual shipping methods via the menu System>Shipping methods and for each one, enter the zone and the weight range (with the minimum and maximum weight fields) for which that shipping method should be in the restrictions section of its options page, and set the price corresponding to that weight range/zone.
That way, the system will automatically filter the shipping method(s) on the checkout to display only the ones matching with the address of the customer and with the total weight of the products in the cart.