Magitech apocalypse. Maybe lots of arcane armour and warforged lying around in ruins, and a few keepers of the knowledge to use these armours. It gives me a very Spellbinder feeling. [Spellbinder being the best Polish-Australian sci-fi show I know of. It is also the only one, but very good nonetheless, aimed at teenager audience]. Armorers would be the most obvious fit.
Battlesmith if they know the secret to power/repair the battlebots lying around. You could fluff the ability to invoke a new Steel Defender with a spell slot as finding a carcass and repowering it. If you want to "up the tier" of the Artificer -- I may be mistaken -- and this is the chosen solution, finding special carcasses with a (slight) power-up depending on what is found (maybe a heavily armoured model with +1 AC or a limited flight ability if you're going to fight winged opponents) could be the way to go without feeling forced and imbalance can be easily corrected (just have the current model be destroyed in a fight).
That would make the alchimist invaluable. If everything is poisonous outside safe haven enclaves, then, depending on the way you handle that, the ability to cast lots of restorations and greater restoration at later level will be more useful than in a regular party. It could hamper severely the party's ability to move without a cleric or artificer, though, so I might not go this way in your situation.
Renaissance guns aren't powerful enough to change things in the type of artificers being useful. Modern guns do change things. They make the battlesmith a very good damage dealer. And since there is no rule for "not knowing how to craft things", the lack of ammo for modern guns is countered by the mundane crafting rule based on whatever tool proficiency you deem necessary (and that the artificer would be in a good position to take). Or, if you want a gritty feeling of counting every bullet, then you can have acquiring ammo an adventuring goal, same as food and water of the nonpoisonous kind.
Would infusion work in dead magic zones? The that don't cast a spell but replicate a magic effect.
Given your setting, I'd say go with battlesmith and armorer, they are the easiest to fluff in a post-apocalyptic setting. The artillerist feels a little to steampunky (with temporary HP dispensing machines...), the alchimist is weak, the maverick is too magical, the blade-using and body-part replacing one from Exploring Eberron and Dread Metrol are thematically unfit.
The obvious choice you need to make if you want Artificers to shine IMHO is to set the "magic item availabilty" at one of the two very specific positions : either they are nearly inexistant, extremely rare old relics of before the Cataclysm -- so the infusion ability, or fluffed as the Salvaging Old Tech ability

is great and useful despite the magic item list being so-so -- or have magic items be not that sparse (just plunder a battlefield...) but have enough downtime for the artificer to create the more "utility ones" among the uncommon.