I agree with trixie. Assuming that you have help then changing the worktop is probably the cheapest solution. There are some very good tops in B&Q that look just like granite,from �60 for a 3 metre(10ft) length.
However purchasing is the easy part because these tops are heavy hence the physical labour bit. Also of course you may need to cut a template for a sink so some power tools may also be needed.
I think the real problem that you may have with some sort of 'fablon' cover as you have already stated is that it almost certainly won't be resistant to heat or to marking or a careles knife cut. So going to all the trouble to cover it would,in my opinion,be false economy. Similarly if you tile over you are going to have serious height and gap issues in the sink area. Not a good idea or a neat solution(only my opinion)as the tiles would require special cutting to fit.