Well, to make a good cross-section depends on a number of variables, depending on what particular interests you may have. For some, it's all about battleships and aircraft carriers, but of course, much of the fighting was done with much smaller vessels, cruisers, destroyers, submarines and such, and of course, the war couldn't have fought without transport ships as well, so you see how this gets tricky! I would break it down by nation, with a few very distinctive ships with a lot of water under their keels, but others would doubtless do otherwise.
USA:
Carrier 'Enterprise' (or perhpas 'Saratoga'), as these were 'the big punch' for most US naval battles, either being present, or certainly influencing the conduct and/or outcome of the battle.
Battleship 'North Carolina,' as this type was involved in most of the surface battles involving battleships, and is a good 'middle ground' battleship between the 'Masschusetts' and 'Iowa' types
Heavy Cruiser 'San Francisco,' as this type and its close sisters were involved in more battles and won more battlestars than just about any other in the US Navy
Destroyer 'Fletcher' This type (along with the 'Gearing' and other classes) was everywhere, and did everything....
JAPAN:
Carrier 'Shokaku,' because it was heavily involved in just about the whole war, starting from Pearl Harbor, and is a good representative, and perhaps best of the Japanese heavy carrier type
Battleship 'Kongo,' because it is perhaps most representative of the Japanese battleships, and was involved in most of the Japanese campaigns. Many people would have chosen 'Yamato,' but those 'super battleships' weren't really involved for much of the war, and accomplished very little at the end of the day!
Heavy Cruiser 'Chokai,' beacuse this is an excellent representative of the Japanese heavy cruisers, that was involved in a variety of very serious surface battles against the US Navy, the ABDA command, etc.
Destroyer 'Yukikaze,' because it is an excellent representative Japanese destroyer whose deadly 'Long Lance' torpedoes inflicted more damage on more warships and were involved in more battles than any other type.
BRITAIN:
Battleship 'Prince of Wales,' because this type is perhaps most representative of British capital ships, and of course this ship and her sisters were involved in MOST of the naval battles involving serious enemy forces (Bismarck battle, Scharnhorst battle, etc, etc).
'County' class heavy cruiser, a variety of these to choose from ('Suffolk,' etc.), because they were also involved in a lot of battles all over the world, from the Bismarck chase, to the Graf Spee battle, and even Guadalcanal!
'Flower' class corvette, because these, along with a variety of American and British destroyers are what fought and largely won the 'Battle of the Atlantic against the U-boats...
GERMANY:
'Bismarck.' Nuff said
Type VIIC U-boat, because it was the primary, most successful, and arguably most representative German submarine
Sorry! I went over the number ten, but there you go; where do YOU draw the line?