I need some advice on laying a New Lawn?

Hi, i need to completely blitz my back garden, the previous owners made such a mess its cant be recovered! Basically im need to either Re-seed it or Re-turf it, first off which is better or is it just down to money? Secondly which everyone i choose i need to remove the existing turf, do i 1) just use a shovel and dig and turn the turf over and then use a rotavator 2) kill the existing gr off with weed killer then use a rotavator on it 3) remove the turf on its own? Any advie would be grateful...Thanks