When you find an infusion, you can choose to use it to improve your health, shield or salts capacity. What exactly do these options do? Will I get more power uses per salt pickup if I improve salts? Will my shield be stronger or regenerate faster, and by how much? How much health will I gain per infusion, and will it make health pickups more effective?
An infusion increases the size of your bar, though I have not encountered any information suggesting what the actual numeric value is. The benefit is definitely getting "stronger". Shield and Health make you harder to kill. Salt gives you more salt to spend on using Vigors. They do not affect your regen rates or the actual gain from a restorative pickup.
Infusions improve your "hit points", basically. More salt? Self-explanatory. More health? Makes you harder to kill. More shields? Makes you more survivable.
Before I go further, let me state that I'm NOT a hardcore, frequent gamer. I'm an older person, retired early, and have far too much 'free' time. As a result, when I'm not playing guitar, I can play some games on my peecee.
I've played BI on 'easy' about halfway through, then just recently completed the game on next-to-hardest difficulty. I spent only two infusions on health, five or six on salts, the rest of them on shield until maxed, then any remaining to salt. If you upgrade things as often as possible, I suggest that you'll find reasonable success using this general formula. Shields are very good to have, and saved my butt many times. Elizabeth will give you extra health when you need it, if you pay attention and grab it fast. She'll support your quest very well.
For what it's worth, then, I recommend doing the most you can to upgrade shield, then salts(for vigors, depending on how frequently you use them), then on health.
Your mileage may vary, close cover before striking, and always pay your lawyer.
Infusions strictly increase your capacity for health/shield/salts. They do not increase the effectiveness directly. Since health/salt pickups are always a percentage, higher capacity = more net health/salts per pickup.
Since there are no health/shield/salt numbers, it is difficult to determine the exact amount per infusion. However, the increase in health is approximately twice as much as the increase in shield.