If this is a shirt for martial arts activity, Cotton/Poly for moisture-wicking and keeping some stink at bay. If this is only for daily wear, Cotton or Cotton/Rayon.

Would you say these weigh any different from the hickory sticks?

I have an older version of this bag: https://www.titleboxing.com/products/title-boxing-champion-sport-bag. IF they didn't make too many changes, this should fit a lot of stuff especially if you're multi-disciplinary. I fit boxing gloves, shinguards, headgear, 2-3 training knives, and at least 2 pair of escrima sticks when I stuff them in there diagonally. Also, a rubber training gun, a mouthguard, and other small stuff. Your results may vary (likely no bokken). Check the specs to be sure.