2000 through 2002 Tundras use Dexron-III ATF as described in your owner's manual. There are several brands of synthetic Dexron-III, with Mobil 1 probably being the most available, reasonably priced, and excellent quality. It takes about 15-16 quarts for a complete flush and renewal, and about 4 quarts for just draining the pan and refilling. There is no transmission filter in the system, only a suction screen. Installing an inline filter in the cooler hose is a good idea. These are available in any autoparts store, about $20-25. Magnefine and SPX Filtran make them, and they work well. You'll need the 3/8" size for a Tundra.
BTW, 2003 & later Tundras have a slightly different model transmission which requires Toyota's Type T-IV ATF. There is no licensed substitute for this. Amsoil's synthetic ATF claims that it is suitable, and many shops use Dexron-III plus a bottle of Lubegard's HFM black-bottle supplement.
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