I'd say find a local tea shop and get small amounts of a couple different types. The tea that makes it to western markets is usually pretty low quality, black teas are the most likely to be decent. There isn't gonna be a huge quality difference between brands either. If you want really good stuff, you gotta order online from specialized sellers, usually from asia.

Also, ditch the tea ball thingy and get a steeping basket or steep straight in the pot, the leaves don't have room to expand in there and you don't get good flavour.

I can try to recommend something more specific based on which flavours you like the most (earthy, woody, chocolate, malty, fruity, floral, vegetal, grassy, nutty etc.)