The most profitable way to get rid of rare equipment is often the Black Lion Trading Post. For common equipment, the trade price is not even high enough to account for the cost to post the item. In those cases, it is more profitable to just sell them to a merchant.
I would just sell them to a merchant unless you really need the materials that they are composed of, the essences of luck, or are working on the monthly salvages achievement. Salvaging armor pieces usually nets less value than simply selling them.
As you noted, currently weapon stats (weapon damage, weapon stats, sigils) do not apply when using a weapon kit. Each weapon kit has its own weapon damage (scaled according to level).
However, ArenaNet has stated they are working on making sigils and weapon stats work with weapon kits.
Best Answer
The staff is called The Crossing.