I think what would help you a LOT through this stage is to have a really good understanding of what life is like from her perspective. A little empathy will go a long way towards making you a happy parent, and thereby making a happy home.
You're right that the anger from being told "no" is stemming from a lack of understanding *why* they can't have or do that thing they so desperately want. But imagine for a moment how the situation looks from her perspective - toddlers live in the moment, they feel intensely. In that moment, putting a rock in her mouth will seem to her like the most important thing in the world, from which she will derive ultimate pleasure. It's an enviably simplistic, hedonistic state of being that they live in. Now to be denied that pleasure, and to not be able to understand why! That sure seems worthy of a tantrum, to me. I imagine all of those moments where I have *just* sat down from doing housework while my son is sleeping, cup of hot tea in hand, ready to finally relax and enjoy some time to myself, only to hear him start to wake up the second my butt hits the sofa. I am not ashamed to admit that I have cried in those situations! I also imagine what it would be like if I reached for my secret chocolate stash, only to have my husband take it from my hand and say, "No." I would RAGE on him - and that's what a child in the middle of a tantrum is going through, only in a pure, uninhibited, completely authentic manner.
Toddlers don't possess the verbal skills to express their emotions, and the result is an overflow of emotion that we see as a tantrum. It isn't a bad thing. It's annoying, it's embarrassing when it happens in public, it's frustrating because you probably don't see what the big deal is, but they are dealing with big, scary emotions and they need help to get through it. They need your calm presence, and when the storm passes they need for you to help them process it, to teach them the verbal skills and coping strategies that will help them next time (for an older child, obviously not a 14 month old!).
Tantrums are real emotions; it isn't bad behavior. It's developmentally normal, and I don't think children should be punished (and yes, I think that ignoring them is a punishment) for simply acting their age. To assist your child through these rough moments doesn't teach her that tantrums get her attention, it teaches her that you will help her through the rough times. Children who are empathized with are more likely to show empathy themselves.
It's a real shame that so many people have such a negative view of children - that they are manipulative, coercive, trouble-seeking brats, and without proper discipline they will become horrible selfish monsters. I have the opposite point of view - I think that trying to manipulate their behavior (through rewards and punishments) contributes to self-centeredness as adults (keeping in mind that young children are, by nature, self-centered); I think that modeling appropriate behavior is the most powerful parenting tool in your arsenal; I think that empathy and the golden rule will get you far; and I think that a lot of kids turn out well *in spite of* their upbringing, rather than because of it.
OP, two books that you might find helpful to understand what's going on in your little one's brain are The Emotional Life of a Toddler and Unconditional Parenting. Happy parenting, and welcome to toddlerhood!