Hi A.,
Here's my two cents: whole milk is appropriate, if not necessary, until age 2 because a child's brain is still developing and not having enough fat in the diet will effect brain development. Switching to 2% or 1% at 2 sounds right.
Organic milk is always going to be better for what it DOESN'T have, namely antibiotics, bovine growth hormone, chemicals in the cow's feed, etc.
In terms of storing it, you need to keep it cold. You might be surprised by your baby liking milk cold. Be very careful about warming milk up in the microwave - be sure to shake it up after heating, and test it on your inner arm or lips to be sure it's not too hot.
If you are in a restaurant you can request a big class or a bowl filled with boiling water, into which you can submerge the milk for a few minutes.
Good luck!