Howdy & welcome. Excellent choice starting with the Tamiya Fletcher. The good news is that the Leutze is a round-bridge as is the kit.
1) References: The Squadron Fletcher Inaction is pretty good. Relatively inexpensive, but out of print. The Squadron Kidd book is also good. There are other hardback print subjects, Anatomy of the Ship - The Sullivans and Raven's Fletcher Class Destroyer. Web has several good sites. NAVSOURCE.ORG is a database of US Navy ship photos. DESTROYERHISTORY.ORG has good info on all USN destroyers, Fletcher-class included. SHIPCAMOUFLAGE.COM includes a database of camouflage measures applied to USN ships as well as info on camouflage history and the measures themselves. Read Allan Raven's monograph on the history of naval camouflage.
2) Pick a date for your subject. The Tamiya kit represents the earliest configuration of the ship class, and then not really the Fletcher at this time period. In this figure on destroyerhistory dot org http://destroyerhistory.org/fletcherclass/armament/ you will see that the Leutze had 10 40mm gun tubes (the bad news). That means 2 twin mounts in tubs ahead of the bridge, 2-twin mounts at the waist abreast of the stack, and a twin in the raised tub between 5-inch gun mounts 3 and 4. Twin 40's in 1:350 scale are available from multiple sources. You will find them in resin + brass from sellers such as L'Arsenal, Flyhawk, and others. Master & BD Barrels sells just brass barrels to go on resin mounts. Check Freetime Hobbies for these vendors.
3) Decals for the Measure 31 camouflage. No not really. Check out Gator's Masks. He sells pre-cut tape masks to paint the pattern. It is a bit fiddley. You apply the whole mask then selectively remove segments, paint, and reapply the segments as you apply more & more colors. Measure 31/16d is called Dark Pattern and it includes 5H Haze Gray, 5O Ocean Gray, and Black on the verticals, and 20B Deck Blue and 5O Ocean Gray on the horizontals. Vallejo/AK has equivalents (though not these names), they used to be available from ModelMaster, and are available in Colourcoats. There is no FED-STD number for these. They went obsolete before the system was established.
You may want to go with the Leutze in 1945, when the camouflage pattern was simplified to Measure 22; 5H Haze Gray over 5N Navy Blue.
4) Rigging. See the references. Most will give you an idea. Flag halyards to the flag bags, radio leads to the bridge and along between the stacks. Mast stays (fore and aft) are about all there are.
5) Hull number decals. Plain white and/or black to contrast with the underlying camouflage, not shaded, located bow and stern. No name painted on the stern. Iron Shipwright, Yankee Modelworks among others make them
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