The big health problem with drinking water (or foods) and plastic is BPA, which, fortunately, is not used in most cycling water bottles.
Some people like the hydration packs because they have difficulty reaching for a water bottle and controlling the bike while drinking. Probably a greater reason however is that they're looking to carry more water, and make the mistake of thinking that the hydration pack carries more. I like to promote the 33-ounce Zefal Magnum water bottle. I and my family put two on the frame as usual, giving 66 ounces, and two more in the holder behind the seat total 132 ounces, which is more than a gallon altogether. This comes to a lot more water than even the very biggest hydration packs, without having to have any weight on your back. If you put another bottle cage under the down tube, you'll have over five quarts--165 ounces. Cleaning is extra easy with the wide-mouth top which is plenty big to put big ice cubes in if you care about that stuff. (Myself, I don't like my drinking water cold.) These have no BPA in them. If you want to supplement these by adding a hydration pack like to go long distances in hot mountains or desert where you won't have a chance to refill for a long time, go for it; but I'd say start with the bottles.
The Zefal Magnum bottle was unavailable for awhile, but is back now. We've bought 15-20 of them and never had any problems with them, but apparently a few people did have leakage problems, so Zefal apparently redesigned it and re-introduced it.