Actually, white tea has least amount of caffeine (also the least amount of time to brew, and the lowest water temp. to brew it in).
I'd recommend something like yerba mate (unsmoked, the flavor takes some getting used to) for the times that you need to stay awake but don't want caffeine. Green teas like sencha and hojicha tend to be milder and easier to brew - very forgiving if you tend to leave the leaves in too long or use water that's too hot (this is called "stewing" and the result is a bitter, awful tasting tea). Genmaicha is my favorite green tea, especially after large meals - it has puffed rice in it that gives it almost a savory, grassy flavor. (tea brands like two leaves and a bud, rishi, stash, and republic of tea are good quality for the price).
Darjeeling is also a wonderful pick me-up, but be careful - it's just like champaign - darjeeling somes from Darjeeling, beware of knock offs.
Tisanes are all of the herbal teas - I'd recommend brands like traditional medicinals or yogi teas for any of your calming/soothing/ready to go to bed moments...and also celestial seasonings has a sleepy time tea that is just plain tasty.
sorry to "geek out" on you all about it (I plan to open my own tea shop someday!)- but i figured I'd put my two cents in
Hope this helps