Free Delivery and Postcode delivery

Hello, im new and finding my way round.

I sell a range of product from small lunch box size items to items the size of a car.
I want to set up free shipping and then shipping based on weight/size and postcode.

I have a shipping app that at checkout you plug in address and it gives a shipping quote, this is done through the pluggin, i dont set any costs etc.

So when i set the products up in the products section i put in the dimensions etc and then i want to be able to select a shipping zone as Free Shipping or The plugin so you get freight at checkout.

I dont seem to be able to do this. I have tried once and it allowed someone to choose free shipping on a large item and i inturn lost money on the deal.

WOuld like some adice if possible.

Thank you in advance