How can I sell my equipment?

I just started playing Dark Souls 2 without playing the first one.

Since I don't see any sell option in any merchant: Can I sell my old-unused-equipment for souls?
If I cannot sell it, does it have any value to be keep until later?

There is an NPC named Gavlan that will purchase items and equipment from the player. He is the only NPC that serves this function.

He is initially found in

No-Man's Wharf

but moves once you've spoken to him. This means that at each location until the final one, you'll only be able to sell to him once.

The second location is:

Harvest Valley

The third and final location is:

Doors of Pharros

Source is the Collector's Edition Guidebook, pg 428.