Then it's down to your cash reserves to get your mitts on the new weapon. Once you meet the requirements for a Signature weapon, simply visit a Trading Outpost and the weapon unlock message will appear automatically. It's no bad thing to have both a one handed and two handed Signature to suit both situations.
One handed weapons can be used while riding vehicles whilst the two handed weapons are more stable but cannot be used whilst riding (or flying). You may not have noticed but there's significance to the one handed and two handed weapons. Signature weapons range from sidearms to SMG's, sniper rifles and LMG's. For example, the awesome Ripper LMG weapon is only unlocked after you conquer 4 fortresses. Each weapon has its own unlock requirements with the best weapons having the most difficult unlock path. Activities range from finding blue masks to capturing a large number of Bell Towers. Further down I've listed the complete list of the requirements for unlocking each of the Signature weapons in the game. All of the signature weapons must be unlocked before they can be purchased but its well worth the effort because of their deadly statistics and modifications.
Far Cry 4 contains a handsome selection of Signature weapons which are classed as the best weapons in the game.