I'll throw my experiences into the mix
The biggest differences you will feel are the torsion bars, springs, shocks and a proper alignment. They make a bigger difference than everything else except tires, BUT, if you put awesome tires on the stock suspension it will actually highlight how weak the stock suspension stuff is. You might turn faster lap times, but the car will feel awful because the body roll and vague handling will be accentuated . Chassis stiffening makes a big difference, but, it's more about how the car feels than how it actually handles.
When I bought my Challenger the first thing I did was rebuild the entire front suspension. I installed the 1.12" torsion bars and XHD leaf springs, upgraded the brakes to 11.75" rotors, installed tubular UCA's and LCA's (overkill), and had a proper alignment done. I left the shocks alone (it had brand new KYB's). The improvement in handling was spectacular, even with the 15" rims and harder than hockey puck Chinese knock-offs of BFG T/A's. Yeah, not even real T/A's. I didn't do any chassis stiffening, didn't install sway bars, didn't do anything else. I put tens of thousands of miles on the car like that before I installed the 275/40/17's on 17x9's all the way around. Again, big difference. The car was much more solidly planted, and I actually got some body roll back now that I could put the grip through the suspension. I probably would have noticed a sway bar upgrade at that point with the 275's, with the hockey pucks it was oversprung without the the bars. I had to switch back to a set of boxed LCA's when my CAP sourced tubular LCA's failed, probably another 10k miles later. Didn't notice any difference at all. I forget when I switched to the Hotchkis UCA's and ditched the CAP tubular UCA's, I think it was actually before the LCA's failed. I did notice the removal of the anti-dive, the nose of the car would bite down a bit more under heavy braking than it did before. Last thing I did was upgrade to the Bilstein RCD's, and I instantly wished I had done it years earlier. It made the car so much more tolerable, the ride was much less harsh and the handling was better.
I never did any chassis stiffening on the Challenger when I had it on the road with over 60k miles logged. Now, with the 1.12" torsion bars and 275's on all 4 corners I can tell you I could FEEL the chassis flex in that car. Which, now that I've torn that car down to the shell, isn't surprising. That car was a rusty POS. It has rust in the frame rails, the torsion bar crossmember, the floor, even in the hardtop structure of the roof. Yeah it's bad. I'm actually kinda surprised I didn't fold that car in half now that I've replaced as much metal as I have on that car, with a lot more to go. But you know what? It handled pretty well. Yes, the chassis flex was a spooky feeling when you really pushed the car hard. And by comparison, I did the frame connectors, torque boxes and J-bars on my Duster pretty early. That car feels SOLID. And that inspires more confidence, and it definitely feels better. But the Challenger still handled well, even though it was even more flexy than a stock E-body, which is worse than an A to begin with.
As far as the K frame stiffening, the steering box mount on the V8 K frame I installed on my Duster was about 50% separated from the K. The welds were fractured, and when you turned the wheel back and forth the steering box would move close to a 1/2" in either direction. The K's on the later A-body's were not welded well. The K on my '71 looked much better, although I seam weld and gusset all of my K frames now. Again, probably not something that will make you faster, but it feels better.
So, I would rebuild the suspension and do the torsion bars and springs first. Brakes should be in there first too. You don't need tubular arms, a set of offset UCA bushings and new bushings everywhere else will be good enough to put a decent alignment on it. Tubular uppers are nice because you can get more caster, which is good, but not necessary especially with a manual steering car. Of course if you decide to do them later it means re-doing work. Shocks can wait some if yours aren't shot but you'll really appreciate the better ones (bilsteins, fox's, etc). Check the steering box mount on the K. If it's ok, you can skip the chassis stiffening until later. If it's not you'll have to fix it and might as well at least do the K. I just finished installing a set of US Cartool subframe connectors on my Dart, and I will say unless you have your car on a rotisserie just make your own subframe connectors. I did that for my Duster, and it was SO much easier. And I don't think they're any less of an improvement than the weld to the floor kind, just about 3 days less welding to do. Tires can wait some, they make a big difference but you need the suspension to really make use of them, and the upgraded suspension will still be an improvement even with smaller tires.
