None of your options are correct.
Here are correct options:
#1 Unarmed Strike +6/+1 (full strength damage), Claw +1/+1 (half strength damage), Bite +1 (half strength damage)
Note: this assumes the body part you are using for the unarmed strikes is not the same limb as one of your claws. If you are then you cannot use the claw on that limb.
OR
#2 Claw +6/+6 (full strength damage), Bite +6 (full strength damage)
OR
#3 Unarmed Strike +6/+1 (full strength damage)
Natural Attacks: Attacks made with natural weapons, such as claws and bites, are melee attacks that can be made against any creature within your reach (usually 5 feet). These attacks are made using your full attack bonus and deal an amount of damage that depends on their type (plus your Strength modifier, as normal). You do not receive additional natural attacks for a high base attack bonus. Instead, you receive additional attack rolls for multiple limb and body parts capable of making the attack (as noted by the race or ability that grants the attacks). If you possess only one natural attack (such as a bite—two claw attacks do not qualify), you add 1–1/2 times your Strength bonus on damage rolls made with that attack.
Some natural attacks are denoted as secondary natural attacks, such as tails and wings. Attacks with secondary natural attacks are made using your base attack bonus minus 5. These attacks deal an amount of damage depending on their type, but you only add half your Strength modifier on damage rolls.
You can make attacks with natural weapons in combination with attacks made with a melee weapon and unarmed strikes, so long as a different limb is used for each attack. For example, you cannot make a claw attack and also use that hand to make attacks with a longsword. When you make additional attacks in this way, all of your natural attacks are treated as secondary natural attacks, using your base attack bonus minus 5 and adding only 1/2 of your Strength modifier on damage rolls. Feats such as Two-Weapon Fighting and Multiattack (see the Pathfinder RPG Bestiary) can reduce these penalties.
In summary, you can combine natural attacks and unarmed strikes but it is not usually very effective.
Three +6 attacks are usually better than one +6 and four +1 attacks (assuming you are a monk and thus can make unarmed strikes with a non-claw body part).I suggest sticking with the natural attacks.
Edit: I was adding why right when Jeraa posted. :P
As Gauss said, none of those are correct. But he didn't say why. Natural attacks never receive additional attacks from a high base attack bonus. If you have 2 claws and a bite attack, you will always only have two claws and a bite attack regardless of how high your BAB gets (unless you have something else that grants additional attacks, like being under the influence of haste).
Edit: And I will stop adding in why as he edited in why as I was doing so.
LOL Jeraa :)