A lot of teas are blends. Earl Grey, for instance, is a blend of black teas—exactly which ones depends on the company you’re buying it from—flavored with oil of bergamot. Irish Breakfast, English Breakfast, Scottish Breakfast, they’re all blends.
This is not necessarily a bad thing, but it suggests a specific direction to go in: unblended varietals. This is where you look at Ceylon, Assam, Darjeeling, Keemun, Lapsang Souchong, and then you look at tea grown on specific estates or at specific times of year—a first flush Darjeeling from the Okayti estate, for instance.
(You don’t need to get that anal-retentive: if you can distinguish between Ceylon, Assam, and Darjeeling, you’re doing better than the vast majority of people.)
And every tea I’ve mentioned in this answer is a black tea. Basically, depending on how long the leaves are allowed to oxidize after being picked, the tea can be a green tea, a white tea, an oolong tea, or a black tea.
My own tea cupboard always contains at least 2 black varietals—lately Ceylon and Darjeeling—some black tea blends, some of them flavored with fruit, and jasmine tea—which is the only green tea I really like. (It’s a blend of green teas with jasmine flowers in it.) I’ve developed a fondness for Scottish Breakfast lately, because it’s heavy on the Ceylon and light on the Assam, and I like that because it’s lighter than English and Irish Breakfast.