I'll try to make my question clearer: I only see three tiers for weapons—d4, d6, and d8. If I use Become Stronger on a weapon that already uses a d8, does it, for example, become a d10, or is it already at its maximum?
As for choosing a magic item, I'm feeling a bit unsure. Considering that the three tiers are Magical Wand, Magical Scepter, and Magical Staff, in my opinion, something like Beginner's Spellbook, Intermediate Spellbook, and Advanced Spellbook would give more of a magical feel. I think it would make one feel more like a wizard rather than just having a wooden staff.
Thanks for the answers anyway!