Keith Baker hit a similar conclusion and similar beats to me on the potential this has for really distinguishing your character and providing unique flavour to your spells and other class abilities. It's worth noting as well that an artificer can be proficient in multiple tools, and whilst they may specialise in one or two, there's nothing stopping them having a variety of options for invention origins.
Please see Baker's post for some examples of this; read on below for some alternatives and additional thoughts on how spells and subclass traits could work with tools in mind. I've left some out but will go back to them in time.
Alchemist's Supplies: Potions, salves, and poultices. Some must be thrown or applied directly to the target; others require mixing just before creation, breaking down and reapplying. You could alternatively go the Fullmetal Alchemist route, though this is likely more a combination of tinker's tools and loosely applied alchemical theory.
Brewer's Supplies: Your tools have given you experience in short hours of work followed by a long duration of waiting for the best results. Your tools can be used to distill and purify. You know just the stiff drink to get a good night's sleep and cure a wound or two along the way.
Calligrapher's Supplies: Baker's ideas of writing the words of the spell or reading them off of paper are solid choices here. Though this may be classified more under painter's tools or an independent tool set entirely, I also like the idea of artificer tattooists, channeling magic through ink and skin, constantly patching up their work as the magic burns out and the ink fades away.
