So I have a War Magic Wizard that just hit level 6 and took a level of Artificer. eventually when I hit third level in Artificer which subclass do you think works best with this tradition? I'm not sure I'm seeing all the interactions, but I is there any way I can make Fire Bolt count as both a wizard spell and an artificer spell?

I can't think of any way for it to count as both at once.  You can have Fire Bolt on both your wizard and artificer spell lists, but you'd have to choose which version you're casting and which bonus you're getting every time.  A permissive DM might let you stack bonuses on your combat cantrip if you're a specialist of that sort - an Eberron wandslinger who's expanded their training, marching into battle in a beaten leather duster etched with defensive runes over their old uniform tunic with a pistol-gripped soldier's wand in its holster at their belt would be bad the **** ass and I'd absolutely allow you a minor boon to combine bonuses from Artillerist and War Magic (especially since the only actual damage buff I'm seeing in War Magic is the jank-ass Power Surge thing), but I'm not your DM and I have no idea if that's your aesthetic.

Elsewise it doesn't really matter since no artificer subclass gets a boost to their spells until fifth level rather than third.  You're left picking between the Eldritch Cannon, the Steel Defender, or the Experimental Elixir at 3rd level.  Of those, the cannon clearly wins as a low-level dip; the Defender doesn't work unless you're a straight Battlesmith since it needs all the HP it can get and we all know Experimental Elixir is moose piss.  The cannon gives you a solid bonus action and as a primarily-wizard, you'll have a million spell slots to burn on ensuring it's up whenever you need it.  You also get Shield prepared for free, if it's somehow not in your wizard book, and if you do carry artificer to five, Scorching Ray and Shatter aren't terrible to have either.

All of this is moot if your DM allows UA content though, at which point you take Armorer, get your free heavy armor proficiency, make yourself a hyper-busted magical Iron Man costume, and you like it.  War Magic is well known for being intensely borked when mixed with a class that offers heavy armor and shields; Armorer gives you the best heavy armor, as well as allowing you to explicitly ignore Strength for wearing it.  Infiltrator armor specifically is stupid good for this sort of combo.  Got yourself silenced?  No problem!  Shoot them with lightning anyways!  Have a magical Samus Aran arm cannon that shoots lightning, or fire, or ice, or whatever else you've got handy at the time!

Gawd Armorer is so dumb.  Awesome, but dumb +_+

Yurei,

Are you a Dresden Files fan by chance?

PS- Either a Mark of Warding Dwarf or a Hobgoblin as a War Mage makes a great sub boss for a BBE. 😏

Heh.  Have read many of the books, and I can see where the question came from.  But no - my vision of the duster-clad wandslinging wanderer is less connected to the good Dresden and more with my long, long history of playing magical gunslingers in old, pre-D&D freeform games.  For me it just fits, especially as I actually quite favor the Soldier background for wizards, more so than the typical sedentary arcane scholars.  More Trigun or Dark Tower than Dresden, though Harry is by no means a bad template to follow.  After all, anyone who can

Nevertheless.  No way of knowing if that's what Snake Mage wants/is doing, so until he confirms or denies that, prolly best not to sidetrack the thread too bad.  Guy's definitely got me thinking more than I should about the idea, though +_+

I am also a big fan of Harry Dresden, which has me mourning how problematic Jim Butcher is being about current events, but anyway ... yeah my War Mage is a soldier, but not the grizzled veteran type, she's actually a small town gnome who came to the big city to study magic and signed up for the army to pay her way. She's a  boisterous drinker and friend of dwarves, but she also loves the small animals that she can talk to and enjoys cutting loose with fiery destruction from above. She's a scout by training, proficient in cartographer's tools and mainly uses Fly and Message to coordinate troop movements. she was recently promoted to Captain due to her part in defending Waterdeep from a dragon attack, but is hating all the extra responsibility and paperwork and would rather be out adventuring.

I think I am leaning Artillerist, but the idea of using a [Tooltip Not Found] as a mount is also really appealing. I think it just comes down to offense or defense. I could probably get my DM to approve the Armorer, but I feel like I personally want it to be balanced a bit better.

Hmm.

Battlesmith is weapon-focused, but only at 5th or higher.  If you're looking to stick with a low-level dip, that might work.  The Steel Defender wouldn't help much at all in combat, but as a way of letting your move more quickly - which tends to be pretty gol-durn important for a scout and ranger (in the military sense of the word 'ranger', not the D&D sense) - the defender being a reliable mount could work well.  Extra Attack at 5th is wasted on a magical combatant, which basically leaves more room for wizard.

Arcane Firearm is obviously pretty baller for casty combat, especially since my read on it is the Firearm die also doubles on a crit, but man.  I can speak from experience when I say that a Defender's ability to act as a tireless night sentry, and its ability to carry saddlebags/packs for you to help with schlepping gear, is super goddamned nice for a character that does a lot of roving and wilderness camping.  Might be worth looking into even if the HP would be too low to allow the Defender to participate in most fights.

We'll see how she goes. She's kind of a backup character anyway. I might stop her at Artificer 2 and make her a shrubmancer.