I have been getting my hair relaxed for 10 years. I am half black and my hair is a weird texture, medium curls but really fine.
Im pretty much addicted to relaxing at this point, but just be aware that it will permanently change the texture of your hair (until new growth comes in, you cannot "grow out" a relaxer) and it will probably thin and flatten your hair maybe more than you want.
And yes, definately make sure the relaxer you get is right for your hair type. Since you have white hair I think you could do the Japanese hair straightening thing, I dont really know much about it though