Many people don't realize this, but caustic burns (NaOH) are more damaging to tissue than acid burns. It is harder to wash off or out of your eyes. The scarring is worse, and they never seem to heal. In any case you want to handle with care!
I wouldn't pour acid into a graduate if there are any visible water droplets inside. A slight residue wont do anything. When you are done, just rinse the graduate in the sink really well. That is too small amount to worry about.

Sodium sulphate is used as fertilizer, a little bit down the drain wont hurt anything.

Sulphuric acid is available at department stores too. They sell bags of the stuff at sears for car batteries.