It's rather simple to confuse Buddhism with both existentialism and nihilism since it lies in between. The no-self doctrine in Buddhism isn't necessarily the opposite of the Hindu atman. It's confusing to westerns due to the lack of better translations. No-Self (anatman (No - Atman)) does not reject the existence of the Hindu Self; it rejects the impermanent aspect of the Self. When we think of the Hindu notion of the Self, we often times quickly identify with the notion of a soul because that's how we recognize alienating concepts with the ones that are familiar to us; hence we tend to think that Buddhism doesn't believe in a soul, which is clearly a mistake (mostly due to English translations of unfamiliar notions of the terms and concepts). It's important to distinguish the three different versions soul that are known to us regarding this topic. The Hindu Atman is rather similar to our western concept of what a soul is - pure and consistent to which we attribute more qualities to it; persistence, essence, unchanging, enduring etc. Anatman is not the rejection of the soul, but only the unchanging aspects. When we translate No-Self, we should always be aware that it's really 'No (permanent) Self'.
In Buddhism, the self is a process self, and not a substance self. A self is composed of the five skandhas. When Buddhists say the five skandhas are empty, it doesn't mean that the five skandhas do not exists, but rather it simply means that they are never permanent. "YOU" still exist, hence the Buddha in his discourses constantly refers to himself as 'I'. "YOU" are always changing; "YOU" are never as you were. "YOU" persists, but "YOU" are never the same "YOU".
Having understood the concept of no-self and that all things are impermanent, clinging leads to suffering and it's a lot more practical than it sounds. Nirvana is simply observing 'what' as 'what' without pertaining your feelings to it. When we cling for things that are 'external' to us, we let that thing have control over us because we become identify with it. We are happy when we have it, conversely, we are sad when we lose it. Buddhism teach to recognize the fact that external objects are not the source of our joy and suffering, but rather it's our superimposition of the object. And having to realize this, we detach ourselves from all that is not within our control.
In opposition to what you think of consciousness in Buddhism, mindfulness is highly emphasizes as the 7th of the 8fold path in which we do not aim to get rid of consciousness, bur rather to investigate it and utilizing it to its full potential. The same applies to feelings that arises within us, in Buddhism, we do not work to get rid of those feelings at all (because as you said it's extreme), bur rather we aim to rationalize it. I believe many Buddhists have been very outspoken about Buddhism's relationship to existentialism and nihilism and ultimately is a little bit of both, and never extreme to one end.
As I've mentioned this many a couple of times in other posts, the practical aspect of Buddhism shares similarities to Stoicism, where both emphasize on self-mastery and discipline as the way to achieve 'goal' (nirvana in Buddhism, which is a state of pure mindfulness and detachment; and in Stoicism it's eudaimonia - tranquility and happiness).
The state of parinirvana in Buddhism is rather hard to describe of its experience, and ultimately to understand it one must experience it - very similar to realizing Brahman in Hinduism if you would. In fact, when you try to describe it in words you would find yourself at lost of it. When I was TA-ing for one of the class assignments for a world religion class and the essay topic was "Describe what it means to be in the state of Atman-realization (6 pages essay)" a student turned in a 6-pages of blank sheet stapled together with his name on it but it was crossed-out. I passed it over to the professor and he graded with an A. Parinirvana is nirvana after death, and in death there is no experience and no sensory because