Why take a body? Why make a Ring?

[Raynor]

Concerning the shapes the valar assumed, it is stated in the Letters:

Originally Posted by Letter #212

It was because of their love of Ea, and because of the pan they had played in its making, that they wished to, and could, incarnate themselves in visible physical forms, though these were comparable to our clothes (in so far as our clothes are a personal expression) not to our bodies. Their forms were thus expressions of their persons, powers, and loves. They need not be anthropomorphic (Yavanna wife of Aule would, for instance, appear in the form of a great Tree.) But the 'habitual' shapes of the Valar, when visible or clothed, were anthropomorphic, because of their intense concern with Elves and Men.

In Sil it says that the valar could choose whether to be without a form or pick an appearance of a male or female

Apparently, they didn't have a choice over the gender of their body:

Originally Posted by Ainulindale, Silmarillion

But when they desire to clothe themselves the Valar take upon them forms some as of male and some as of female; for that difference of temper they had even from their beginning, and it is but bodied forth in the choice of each, not made by the choice, even as with us male and female may be shown by the raiment but is not made thereby.

[mormegil]

Regarding the body I agree that it was to have influence and control in the physical world.

Regarding the ring, we can easily see and know that by pouring his power into an artifact his power increased more than the original value. But why a ring? A couple ideas I had is the concept of a ring in the representation of something intimate like a marriage. Sauron had pledged himself to this cause and essentially created a marriage convenant...it's a bit of a stretch but understandable too. Also, rings are not easy to loose if they fit you and you don't take them off. Generally they are easy to guard and you always know it is on. Also it's, especially Sauron's ring, is a fairly innocuous object and doesn't immediately draw attention unto itself.