Where did you get the idea that Romans were scared of the sea from? As you point out, they got along fine in the Mediterranean. Roman ships traded extensively throughout the Mediterranean and beyond, and the Romans were able to achieve naval victories against the Carthaginians (who were known for being excellent sailors) during the First Punic War. These aren't things that one would expect from a populace that can't deal with the sea.

I think that rather than 'scared', the point is more that the Roman culture wasn't naturally a nautical one; the Phoenicians and Carthaginians did most of the trading in the Mediterranean in the early Republican era, while the Roman conquest extended primarily on the land. It was only when it was required for war (versus Carthage) that Rome created its first fleet, and wasn't that successful with it...or the second one...but hey, third time lucky! So I see it as not necessarily a fear of the sea, but a cultural disinclination?

Re. the difference between the Med and the invasion of Britain. The Mediterranean, to both the Romans and Greeks, was seen as "Our Sea" - Mare Nostrum - but the amount of myths and legends about it does still show how the dangers were viewed; think of Odysseus' brush with Scylla and Charbydis, or the legends of whichever idiot of the Clodii it was that threw the sacred chickens overboard and brought on a storm. However, it was still their sea, their territory. If treated with reverence, it would be sailable. Past the Pillars of Hercules was the end of the world and the the territory of Oceanus, and was therefore a different thing to Mare Nostrum.

In light of this, I think your point about Caesar's success - and, later, Claudius - was that Oceanus was revered as a powerful god, and therefore the victory wasn't just over the land - they had to fight to even get to that land! The conquest of the sea is mentioned in a lot of victory speeches, and while it can be seen as a cliche, it can also be seen as a very real fear. Caligula's men picking up seashells can also be seen in the light of the "conquest of the sea", making his actions a little less frivolous.