I've written fairly extensively about the British navy here, so I'm going to link you to a few answers below, but let's take your second question first:

was this due to simply the size of the fleet or did British naval officers have exemplary tactical and strategic skills?

Saying that it was due "simply to the size of the fleet" is kind of putting the cart before the horse, because the British were able to sustain a large fleet due to expertise at administration. The boring stuff, like administration, a victualling system able to sustain the fleet overseas, a strong system of naval dockyards and repair facilities, and a relatively solid naval administration, are more important in the long run than simply skill of mariners and officers.

I wrote about this more in this older thread. To quote from that a bit:

• English (and later British) naval administration developed early, and was fairly consistent (in role if not in name) from the time of Samuel Pepys until well into the Napoleonic period, and after. The idea of having a naval administration that gathered under its wing at various points all the details of victualling, supplying ships, building and repairing ships, supplying ordnance, cordage, tackle, and stores, manning, and various other roles was important in naval development. (Note that this doesn't meant that the English/British government controlled all of this individually -- it still contracted with private individuals for many of these services.) Possibly the most important development related to this was having one single Admiralty budget, so that Parliament would have a good idea of the cost of a navy year-over-year.

• A shipbuilding tradition that was quick to innovate. English/British shipbuilders were relatively quick to adopt technological changes from around the North Sea. The French, by contrast, probably had a better academic understanding of seamanship from their universities, and were ahead of their competitors in hydrography and related marine sciences. They did not, however, move as quickly as their English counterparts in adopting innovations such as the wheel (replacing the tiller for steering); my resource has escaped me for the moment, but if memory serves, the French did not install wheels on their ships for almost 100 years after the British had them.

• An established infrastructure for repairing and storing ships over time. The dockyards at Deptford on the Thames were established by around 1500, with a basin being added to the drydock and dockyards in 1517. Deptford fell out of use as traffic increased on the Thames, but companion dockyards at Chatham, Sheerness, and eventually Portsmouth kept up the tradition of having sophisticated repair and building facilities that were ahead of England's and Britain's naval competitors.

• A tradition of seamanship that developed concurrently, and later independently, of the military (army) tradition of the country. Although early English naval organization mirrored that around most of northern Europe, with a soldier as "captain" of a ship and a sailor as "master," the increasing specialization of the marine arts and the change from "land battle at sea" to actual naval warfare meant that the "tarpaulin" or seaman came to command ships, and, eventually, navies. (Compare this to the Spanish example, where the duke of Medina Sidona, the commander of the Armada, had rarely been to sea and suffered debilitating seasickness.) English and British officers went to sea as young boys, and got a practical education in seamanship that was lacking in other countries.

• A store of manpower for ships that was larger as a percentage of population than most Continental countries -- as an island nation that depended on trade, England/Britain had a repository of seamen that could form the core of even large ship companies when they enlisted or were impressed.

• An overall commitment to the Navy that was not present in much of Europe, where armies would be decisive. Britain could not survive as an independent nation without a navy, and has in fact been invaded from overseas several times -- that fact was not lost on Parliament during the wars of the 17th-19th centuries.

Here are some threads that may provide you with further insight:

• Ship Design and Construction in the Age of Sail

• Classes of Vessels during the Age of Sail?

• What changes occurred in the construction, armament, management, and use of warships from the Anglo-Dutch wars up to and including the Napoleonic wars?

• How did a person become an officer in the British Navy around the era of the Napoleonic wars?

As to your first question, the rough "top five" navies of this period fluctuates somewhat, but the major contenders for the title would be the British navy, followed in some order by the navies of France, Spain, the Netherlands, Russia and Denmark. Much of the role of the British navy in the period was defeating threats from combinations of those navies (conversely, much of the French plan to defeat Britain was to combine their naval forces with those of a third party and to defeat the British fleet in detail).