How do we focus on stress for the first noble truth? Do we focus on suffering as the suffering we're experiencing in the present moment or do we focus on suffering how the Buddha and Sariputta put forth and analyzed the four noble truths like: "Now what, friends, is the noble truth of stress? Birth is stressful, aging is stressful, death is stressful; sorrow, lamentation, pain, distress, &amp; despair are stressful; not getting what is wanted is stressful.[2] In short, the five clinging-aggregates are stressful."

Do we just have to notice the actual mental experience of suffering as cause by craving or can we notice all its different manifestations, like the stress of the body or the stress of impatience?
The first noble truth is realized at the moment of anuloma-ñāṇa - the moment before attainment of nibbāna. So, you don't actually contemplate it before that point. Up until that point, you are practicing what is called pubbaṅgamagga or the preliminary path. 

There are four basic ways of understanding suffering:


dukkha-vedanā - suffering as a feeling
dukkha-sabhāva - suffering as a fact of life
dukkha-lakkhaṇa - suffering as a characteristic of phenomena
dukkha-sacca - suffering as a truth


Ordinary people see suffering as a feeling, and thus try to escape it by running away. 

Eventually, some people begin to see it is a fact of life, not to be avoided but to be understood. 

Some such people actually undertake to do so and, as a result, begin to see that suffering is actually an intrinsic characteristic of arisen phenomena; not simply because certain phenomena are painful, but because all phenomena are impermanent. 

Finally, some who see thus will proceed accordingly until realizing in a momentary flash of insight that all arisen phenomena, even those one has not yet experienced, are suffering. This is what it means to realize the truth of suffering. The next moments involve the attainment of nibbāna.

So, to directly answer your question, all phenomena are to be seen as they are (yathābhūta), rather than focussing on those phenomena that are stressful. In the end, one comes to see objectively that no phenomenon is sukha (satisfying), and lets go of them all.