I'll take the liberty of recommending the recently-released Dragon U.S.S. Arizona in 1/700. It's probably the nicest kit in that scale I've encountered. It features turned brass gun barrels and comes with a sheet of photo-etched detail parts (including handrails), and the aircraft and boats are molded in clear plastic. (Paint everything but the canopies and windows.) The price is a bit high for a model of that size, but if you can handle that the kit will give you many hours of pleasure.
Other good recent kits in 1/700 include the Tamiya U.S.S. Missouri (the best rendition of an Iowa-class battleship yet) and Prinz Eugen. For that matter, virtually anything offered by Tamiya is a pretty safe bet. I'm also a fan of the Italeri range (sometimes sold in Testor's boxes). Their H.M.S. Hood and Graf Spee are beautiful - and generally quite a bit cheaper than the Japanese lines.
That scale is a good one if you plan to buid up a collection in a relatively small space. On the other hand, it's awfully small - though in recent years, with the help of photo-etched detail sets, modelers have done some astonishing things with 1/700 kits. If you want something a bit bigger you might consider going into 1/350 scale. There are some fine battleship and carrier kits in that scale (most notably the recent offerings from Trumpeter), though, as one of the other participants has noted, they tend to be pretty expensive and take up quite a bit of space. A terrific way to start in 1/350 would be the Tamiya destroyer U.S.S. Fletcher. It's a nice kit, isn't terribly expensive, doesn't involve a great deal of repetitive work, and doesn't take up much space. Gold Medal Models offers a really spectacular aftermarket photo-etched detail set for it, too.
Hope this is of some use.
Youth, talent, hard work, and enthusiasm are no match for old age and treachery.