How prepared was England for invasion in 1588?

Adequately, at least in naval terms. Better ships sailed by better seamen. The tactic of harrying the Armada so it kept moving downwind was a good one.

However, had the Armada got a bridgehead and the Spanish troops in Holland got across things would have been distinctly dicey as the army was not too good.

It wasn't that well prepared at all. Safe to say that the British navy gave a good account of itself in a skirmish, because its ships were much smaller, faster and more maneuverable than the Spanish galleons. However, the real victor was the great storm off the southern coast of England, which wreaked more than a third of the Spanish fleet and severely damaged the remainder so it was no longer considered viable to fight the British fleet, much less attempt a landing.

They weren't. The British fleet was created quickly (which helped it win because the style of its cannon were more modern and effective) to respond to the crisis. In terms of land forces, England relied on local militias. By the time the English could had marshaled a land force to rival Spain's invading army, the Spanish would be drinking port in the Tower of London.