There is something I need to clarify. The purpose of our learning Buddhism is to distance from suffering and attain happiness. However I do not mean that motivated by death means we must be fearful of death. If we can overcome death by fearing death, then we should all start fearing death together

. Of course that is not going to work. In fact fearing death shows that we are still attached to our life and are afraid of losing it, that we are in bondage. This kind of attachment will only make us trapped in the cycles of Samsara and therefore we seek to transcend it, by recognising Death and conquering Death through the dharma.
By recognising that death happens to everyone, just as Shakyamuni Buddha recognises that there is Birth, Ageing, Sickness and Death, one who has wisdom will see that all things are impermanent and will seek the deeper truth rather than wasting their lives trapped in Dukkha & ever unsatisfactoriness. They will find the truth that sets us free from all bondage, all sufferings, and attain the highest bliss. In fact we all can attain the highest bliss in our lives, as the Buddha has shown and said, Nirvana is the Highest Bliss. The Bliss of Nirvana is the Bliss of Clarity, one who truly tasted it will jump with joy. We do not necessarily need to go somewhere else in an afterlife to experience it, but right here and now.
Back to the question of suffering. Suffering is not only in death, death is only part of life, human life is full of various distresses. (see:
The Eight Distresses), in fact sentient beings are almost always suffering from Dukkha unknowingly. However, the Buddha also promised that through the dharma we can find the greatest bliss that is beyond temporary sensual pleasures, unstable, subject to impermanence, unsatisfactoriness and dukkha (see:
http://buddhism.sgforums.com/?action=thread_display&thread_id=171090). As long as there is any form of clinging to and craving for anything - whether enjoyable or painful - one will have dukkha. Any form of mental negativities,
anxious, despairing, frustrated, irritated, upset, disappointed, discomfort, anguish, painful and disgusted, is also dukkha.
Also, regarding 'motivation'/'aspiration', different people have different 'aspirations'/motivation for walking their path.
For example, those who yearn to be free from Samsara can be considered Sravakas, leading to Arhantship:
One who is afraid upon seeing the suffering of samsara
And yearns to achieve nirvana
But has little interest in benefitting sentient beings—
These three are the marks of the Hearer family.Those who have great compassion to liberate all beings and lead them to supreme enlightenment are walking the Mahayana path, leading to Buddhahood. Their aspiration includes saving both the inner sentient being and the outer sentient beings.
According to Mahayana, although Arhants are freed from fetters, they still have subtle discriminations of nirvana and samsara, they cling unto the Nirvana dharma and are fearful of returning to Samsara. A bodhisattva transcends that and returns to Samsara to save sentient beings and further cultivate the Paramitas until they attain the Complete and Perfect enlightenment of the Buddha.