My best weapons experience came from my Muay Thai instructor. I was very lucky to have the opportunity to learn from him. He was also a body guard for years. He worked for many very important people in countries that were less than safe. Very high speed jobs. He's applied his knowledge numerous times under many conditions. He could disarm pretty much anything from you. Pretty cool.
I learned stick fighting from Kali. But I learned the most after class when a handful of us would gather with our two instructors and practice 'real' stick fighting.
I learned a lot of knife fighting from a phillipino guy I trained in submissions.
Anyway, Kali/Arnis/Escrima is a good place to start because many dojos will begin your training with weapons. The philosophy being that the weapon is an extension of your own body. Since you begin your training with this high speed movement of sticks and the threat of blades, you learn to fight in a very high speed environment. Then you train with empty hands and its like evertyhing is moving in slow motion. Its like being a racecar driver for a while, then getting back on the street where the speed limit is 1/5 that which you're used to. Avoiding an accident, or manuvering around problems or situations seems like absolutely nothing. Hmmm, kinda off topic sorry
Like Danielson said, your opportunities to truly learn practical weapons combat are going to be slim because you can't really spar with blades or full contact sticks. There are people out there that do train in full contact stick fighting, in which much of true Kali goes right out the window. There is a void created when you train with weapons(the void of actual impact). This void is typically filled by dance moves, or useless attacks on the weapons themselves. Finding someone willing to teach true weapons tactics may be hard, but well worth it.