Well, I was educated as a chemist, though I work in finance now.
The most important advice that I can give is always protect your eyes. Goggles are the best and they usually fit over prescription glasses. And be sure to wash your hands if you need to remove your goggles to scratch. Also wear rubber gloves - the heavy duty black ones that are sold in hardware stores. A rubber apron will protect your clothes to protect your body is good, too (I skipped this when working in labs as I wore a lab coat and we had safety showers).
Don't worry about adding water to the traces of acid left in your graduate cylinder when cleaning. It won't be a problem. And clean with plain water - it's cheaper than distilled.
You can handle sulphuric acid safely if your careful. But really take care to keep it away from children. A locked cabinet is best.
This reminds me of a reaction I had to run one in hydrofluoric acid - I used plastic because it was so acidic that it would dissolve glass. Now that was very nasty stuff.