This isn't meant to be exhaustive, but I continued to see so many questions on this subject that I thought I might as well try and compile everything I've posted elsewhere. This little guide will cover the Bestine voting, the mission available after, and what to do with the loot dropping off of the Boss Tuskens.
First things first, you need to vote the proper politician into office, not once but twice in order to receive all of the items. Approximately every 30 days, your server gets the chance to vote for who runs Bestine. Your choices are either Victor or Sean. Both of them reside in the Capitol Building, the vote itself is pretty self explanatory if you have a conversation with them.
If you vote for Victor, there is a stronger Stormtrooper presence in Bestine and a special quest originates with Victor in which you go to Fort Tusken and take on the Tusken Executioner (200k HAM/80% resists). If you're lucky enough to get the right loot (more on that below) you can return to Victor for a rifle that can't be crafted.
If you're lucky, you can loot the Tusken Executioner Head and take it back to Victor for your reward, the Lithitanium Rifle. In addition to the Tusken Head, you may also receive one of the following items:
1. Carved Stone which gets you the special Marauder Armor with 75% resist, chest piece only.
2. Smooth Stone which gets you the Lithitanium Carbine.
In order to receive either of the above, you need to have your server vote Sean into office for a term, then get lucky and find the right merchant spawn near the city wall. Trading either of the stones to the proper merchant will net you the stated loot.
And last but not least, there's the mythical Tusken Bones. This is rumored to be in game by some, but has yet to be proven to exist in game by any. The story goes that if you turn in the Tusken Bones you'll get the Junti Mace. It's in the .tre files, but we all know that doesn't mean it actually exists.
And there you have it. Like I said, this isn't meant to be an exhaustive guide, simply an answer to some of the more common questions on what loot gets you what reward. Enjoy!