We have four models for casters: 1/3 caster (sub-classes: Arcane Trickster/Eldritch Knight), 1/2 caster (Paladin, Ranger), full caster (Wizard, Cleric, etc.), and whatever the heck Warlock is.
I don't like a full class being 1/3 casters. That's something that should be reserved for kits of otherwise non-magical classes as a way to grant them some advancement without either having to multi-class or when the DM otherwise doesn't allow for multi-classing. Any class using the 1/3 casting has magic as a tertiary concern and would, implicitly, have less magical acumen than a Paladin or Ranger -- essentially, a dabbler.
The Artificer is clearly not a dabbler in magic, even if their primary focus is not on spell work. That means that the least appropriate answer is for them to be a 1/3 caster. If you want to run with the idea that they are focused on magical engineering, at the cost of full spell capability, then 1/2 caster is an appropriate choice. The Artificer can still have abilities that make the spells augmentation, just like Ranger and Paladin. Also, the multi-class Wizard/Artificer takes as much of a caster progression hit as would the multi-class Druid/Ranger, which seems about right.
A case could be made for a full-caster progression of Artificer, since the Artificer really is based around faculty with magic. I think this case is weak. The focus of the Artificer is magical craftsmanship, not raw magic via casting. The comparison to engineer vs. scientist is very appropriate. One could make it work by creating a bunch of new spells, but those would exist in an almost completely separate, parallel silo from the existing spells.
Personally, I've always liked the idea of using the Warlock framework for Artificer, because it's separate from a "normal caster" and seems to model the "I'm getting better at everything, not just adding some space at the top" quite well. Additionally, the Invocations model could be used quite well for Infusions that gave the Artificer things to do with their spells, like creating short-term potions, improving weapons/armor, etc. without reinventing the wheel and the sub-class pre-requisites for the Infusions is already an established pattern. Finally, the 6-9th level slot the Warlock gets could, optionally, be brought over to the Artificer depending on how the rest of the core class abilities played out -- it's even possible that only a single sub-class (Wand Master, maybe?) would even get that ability. It gives the best of both 1/2 caster and full caster.
So, there are some arguments around building the Artificer. Short form of each, in order of preference:
1) Warlock: Best framework for a class that does weird magical things without spells and by modifying the way spells are applied.
2) Half-caster: A very acceptable framework for a class that is competent with magic, but doesn't necessarily focus on casting.
3) Full-caster: Not crazy, but doesn't leave enough room for non-casting abilities that the Artificer would have without mostly custom spells.
4) Third-caster: Exactly wrong solution and horrible design. Should be reserved for only sub-classes that dabble without multi-classing.