Exactly what power did the Ring of Fire give to Gandalf?

[Knight of Gondor]

I believe that it enhanced his physical capabilities (the instances already mentioned by many, such as the fire used to fight the Nazgul or wolves, but also the "bright flash" and smell of gunpowder when the Goblins were attacking in The Hobbit), but its greater power was in kindling the hearts of men. Hence, inspiring the hope that he did during the siege of Gondor. But I believe its greatest potency was displayed in events such as the healing ("kindling") of Theoden to go to war, or even inspiring an otherwise uncourageous hobbit to run out his door and join a band of dwarves to Erebor.

Let us not also forget that it gave Gandalf insight into the minds of Galadriel and Elrond, the other bearers of the rings.

I thought that Appendix B stated more about the rings, so I shall go and read it tonight.

[The Might]

Still strangely it seems only few felt the power within Gandalf, enhanced by Narya, at least before his return as Gandalf the White:

"...but his joy, and his swift wrath, were veiled in garments grey as ash, so that only those that knew him well glimpsed the flame that was within. "

[Legate of Amon Lanc]

Originally Posted by The Might

Still strangely it seems only few felt the power within Gandalf, enhanced by Narya, at least before his return as Gandalf the White:

I think that reflects the fact that to most, he looked like a simple old man clad in grey. If we use one sentence right from the very beginning of the Hobbit:

Originally Posted by The Hobbit

All that the unsuspecting Bilbo saw that morning was an old man with a staff.

I think this is what most people saw. But on the other hand, the fact that they could not recognise the power in Gandalf, does not mean that they could experience its effects. As it is said about Gandalf even before he got the Ring, in Valinor

Originally Posted by Valaquenta

for though he loved the Elves, he walked among them unseen, or in form as one of them, and they did not know whence came the fair visions or the promptings of wisdom that he put into their hearts.