In Andrew Marvell's "To His Coy Mistress," what kind of love or qualities of love is the speaker trying to express in the first section of the poem...

The first section (lines 1-20) of Andrew Marvell's "To His Coy Mistress" describes an idealized love free from the confines of time or human mortality. The narrator of the poem discusses at length what love might look like if he and his mistress had unlimited amounts of time to develop their affection. The key lines in this first section are "Had we but world enough and time" (1) and "My vegetable love should grow / Vaster than empires and more slow" (11-12), as they illustrate that the narrator yearns for an idealized love in which youth lasts forever and lovers are permitted eons to court one another. 

Marvell later contrasts this idealized love with reality. More specifically, he identifies the fact that youth and life do not last forever, and so he and his mistress are not able to enjoy each other's company forever. Juxtaposed with the reality of finite time, the first section of the poem takes on a rather melancholy tone, as it illustrates the yearning for an impossible love that cannot be realized in the face of human mortality.