I am partial to the maltier Assam teas, the main ingredient in English and Irish breakfast teas, and to the brighter, almost lemony, Darjeelings. I frequently add just a pinch of Lapsang Souchong to the Assams. Lapsang Souchong is the smoked tea that makes Russian caravan blends so distinctive.
I almost always have on hand some genmaicha, the green tea with roasted brown rice and popcorn that is so common in Japanese restaurants.
Lychee black and jasmine tea are also almost always on my shelf, usually whatever brand was available in whichever oriental grocer I was shopping in at the time. Jasmine tea may be made with black, oolong, or green tea. I like them all but prefer the green. (The Chinese products I buy have more Arabic script on the can than Chinese characters.)
I like the occasional addition of spice, cardamon, clove, or stick cinnamon. I prefer the spice to be at the hint level but also run it up to sledgehammer effect. (Many of the farm country bodegas in California will offer a brew that is just well steeped canela, the Mexican bark that is similar to, but definitely not, cinnamon.)
French press coffee pots do a fine job of brewing tea, and I will use mine when brewing for several people, but I mostly use a mesh basket or just throw the loose tea into the mug. I find that the tea is ready to drink when the leaves have lost buoyancy and dropped to the bottom of the mug.
I bought most of my teas from specialteas.com until they disappeared, have yet to find a replacement vendor. I enjoyed specialteas.com for their selection of teas from individual estates.
Finally, the winter favorite: very strong Assam heavily dosed with honey, lime juice, and black rum. An alternative is strong black tea "sweetened" only with whiskey or brandy.