When handling acid, use a method that works for you and minimizes risks, such as floating the container on the pool water and pouring an estimated amount, or doing your measuring down around waist level, and things like that.
Definitely protect your eyes against an errant drop of acid (or chlorine). Proper safety glasses are best, or at the least big sunnies. It's amazing how far a drop can fly. A drop of chlorinating liquid or hydrochloric acid in your eye can do a lot of damage.
Skin though is not such a big deal. Just rinse reasonably soon, i.e. don't run or jump in the pool. It takes a remarkably long time (several minutes or more) for 32% hydrochloric acid to leave a mark on skin. In landscaping/building, I've had it on my skin many times and never seen a mark. It will mark stone (or clothing) much faster. Point being, take your time, maintain control, put things down safely, then go rinse your skin.
The fumes are a good warning sign to stop what you're doing. You'll react very strongly to the fumes, which is excellent defense. The debate about using a respirator with acid cartridges comes up occasionally, but that would likely just defeat your best defense mechanism: smelling it and knowing there are fumes near you. The effect is acute without long term effects, and strong enough that you remove yourself from it right away.
You can virtually eliminate the fumes by watering it down to half strength, but you need to save a few empty jugs and it adds an extra step/complexity. If using this method, you'll be pouring twice as much when you're adding acid to the pool.