The most successful iron man run I did was a stealth SMG with Quick Tinkering, Sure Step, and Pack Rathound to carry a ton of traps and caltrops. Eventually I got Thick Skull at level 12. I eventually died in the Balor zone which was a tragic but totally preventable death--I got spotted because I got careless, but even after I got spotted, I could probably have survived if I hadn't panicked and done several stupid things in a row.
I pay a lot more attention to defense when playing iron man. Less minimaxing and more points to CON. I will say playing super cautiously gets tedious after a while. This probably contributed to my carelessness above. Underrail is a long game.
I think SMG + Quick Tinkering is a good iron man build. Quick Tinkering is one of the most powerful feats in the game. I also like Thick Skull once you start facing things that stun (not many of these until you're through depot A).
My son has gotten to Core City in iron man mode playing a heavy armor assault rifle character, that seems to work pretty well too.
Funny that you should mention this, because these are the exact two builds I have in mind.
SMG-Quick Tinkering:
SMG, Grenades/Throwing, Traps, Stealth and high Con. Super initiative (also Gunslinger for this alone), tons of explosive options, good HP pool, decent evasion, weak armor, mediocre damage drom SMG. Got to lvl 10 just now, but foolishly died to stealthed Lurkers. Trying to dodge an assault rifle burst point blank was not a smart idea, should have used a grenade.
Assault Rifle-Heavy:
*If* I can be bothered to start again before the expansion I will use this. 10 Con, Assault rifle, Juggernaut, maybe stealth also, maybe not. Lack of mobility is major pain, getting hit first in all fights is horrifying, so I am not sure if Ironman is possible.
(Burst-firing weapons are probably OP. Should nerf maybe the Smart-ness of the attack, perhaps.)