+1 on the drink tube cleaning brush. Well worth the price, just make sure you get the right size (the one for hoses that attach to bladders, not for the larger diameter, shorter length straws that go inside the bottles).

I don't find the big brush very useful. Doesn't get into the corners. If you can buy the tube brush separately, that's what I'd do, but they may sell them only as a set. Best way I know to clean the inside of the reservoir is to shake a few tablespoons full of baking soda into it, then put a damp (not wet) dish rag inside, close the stopper and shake vigorously. The baking soda will coat the damp rag and act as a mild abrasive to scrub the inside of the reservoir. A little baking soda on the drink tube brush helps, too. Then just rinse and hang it on a clothesline with something inside it to separate the sides (wooden spoon, spatula, chopstick are possibilities depending on the size and shape) so it can dry completely.