Disposing of large items – Is Sodai Gomi the only option?

So I need to get rid of an old battered suitcase, its big and still too sturdy to smash up (both handles broke, which is why its no good anymore) and maybe a few other items such as a large backpack.

I looked at the Sodai Gomi website but being honest, I didn't really understand it – So is that my only option?
What else could I do?

Also, can basic clothes and maybe some shoes go in the normal combustible trash?

(EDIT: I'm in Minato-Ku, forgot to mention it earlier)

Thanks.