Answer:
Welsh Rarebit can be made with any hard cheese, though in Wales Cheddar is usually preferred. (Caerffili and Red Leicester are also common).
The recipes vary considerably from place to place: beer-based sauces predominate, but there is also a béchamel variety (which is more often found in restaurants).
Some people even believe that cheese toasted on bread qualifies as Welsh Rarebit. In Wales cheese on toast is a completely separate dish, which is called Caws Pobi.
A Different Opinion
You can make Welsh Rarebit by putting a few pieces of toast in the grill and put some chese on it. (Which ever cheese you prefer will be the best)