To make an easy, quick pot of hot water for tea, I let the water run through my coffee maker without any filters. If you also use your coffee maker for its intended purpose, make sure that you do a couple of rinses before relying on the hot water for your tea consumption. This makes as much hot water as you want and keeps it hot while you take your time enjoy your whatever your cup of tea may be.
I too have found that loose leaf tea is the best. Even if you have a bag tea, try seeping the leaves loose. You'd be surprised at what a little 'swimming' does for the flavor. Try to never oversteep or use water that is too hot. You'll be rewarded with a more flavorful and less bitter cup of tea.
As legend has it, one day in 2737 B.C. the Chinese Emperor Shen Nung was boiling drinking water over an open fire, believing that those who drank boiled water were healthier. Some leaves from a nearby Camellia sinensis plant floated into the pot. The emperor drank the mixture and declared it gave one "vigor of body, contentment of mind, and determination of purpose."