Kajukenbo
Israeli Krav Maga
Bujinkan
AKBAN
Escrima
Silat
European Martial Arts
The only common martial arts I can think off the top of my mind which incorporates both striking and use of weaponry are Escrima and Silat. Wing Chun is more of a hand to hand based martial art in which the majority of the strikes involve punching, some kicks, but it includes the use of Butterfly knives and the long pole.
What are you learning for? Do you want it for health and wellbeing? Do you want it for sport? Do you want it for self defense?
Tai-ji-quan Dao is good for health and focuses on swordsmanship, but is for a large part only a health related martial art and is useless for fighting unless you have many years of experience under your belt.
Wushu has all of them and teaches you weapons, but for the most part most of what is taught is useless for a real fight. (I was told this by a martial arts master in China, so it's not only personal opinion.)
FMA (Kali, Escrima, Arnis) are excellent for a mixture of sport and some good basics for self defense.
Krav Maga is good for self defense.
Decide why you want to do it, and that will help you make your choice easier. Also, look around and see what's available. It's worthless finding something you'd love to do, but can't find a place to learn it.
Edit: From what I've seen Sanda is taught as a separate art aside from Wushu. Wushu is more of a dance and Sanda was made for actual self defense and fighting matches.
Don't learn how to fight with any weapons that you don't carry with you on the street. It's useless to train with the Katana if you don't carry a katana with you, because you'll never use it in self-defense. I recommend Krav Maga or Kajukenbo. Systema uses the right weapons, but overall isn't a very effective style.
My chief recommendation would be Wushu. You learn Sanda for fighting and forms are hands and weapons.
Traditional Muay Thai has weapons, but no one teaches it since the money is in competition.
Bujinkan has lots of hand to hand, hand to weapon, weapon to hand and weapon to weapon if you like that stuff.
Aikidou is similar, but less useful.
What do you mean? Be specific.
All Martial arts has weapons, the minimum is your fists and legs.
Kickboxing and kali.
Jeet kun doo
Am looking for martial arts with lots of kicking, boxing that involves weapons training but no shrine stuff.
