Heh, you are a bit like me when I built my previous system, traumatized by noisy systems and wishing for the other extreme.
You could slap on 12 ULNs but I'd think you're crazy! Not that there could still be some benefit... But the stock fans are very good. I wouldn't be surprised if the ULN makes as much noise, at least subjectively, as the GP-14 when moving the same amount of air (GP-14 is rated at 17 CFM more, off the top of my head).
Once you go to the better fans, the exact brand and model doesn't change that much, it's a tradeoff between low noise and high RPM+high airflow. How you mount the fan (eg. ready to rattle hastily screwed against a grille vs using the silicone mounts that come with Noctua fans or with dampening pads) could have more effect than a choice between two similar models. Key is to run them at low power though, rev any fan up and it will make some noise.
All mounts are designed for 140mm, except maybe if you have a small CPU cooler
Basically there is 2 x front, 2 x bottom, 3 x top and 1 x back. One more for the side if you don't take a windowed case (I like mine, stylish and practical)? I would think 3-4 fans or so is optimal, maybe 5. You will want at least one fan in the rear and probably one in the bottom (airflow+openings). Key decision is do you want to have the top slot(s) open. The hatches are dampened and less noise will escape if you leave them closed.
The Define R5 is quite versatile, somewhat large, well equipped case. You can build it up for a quiet computer, high airflow, or both. How much cooling you need depends on the components used and their TDP. 980ti has high TDP (especially the MSI model) so probably you'd want 4-5 fans, maybe more if you use ULN or low noise adapters? You will need to ensure decent airflow.
Introducing water cooling is taking it one more step hard core, it could be an option but you would need to research it, I am not sure if you get much reduction in noise unless it's very specialized kit. I'm pretty sure air cooling would be sufficient as such, but it depends on how high you let your components go, if fans are running full power there will be some noise.
BTW the ULN is a DC model fan, same as the stock ones. I'd prefer PWM ones as they are easier to run smooth from motherboard connectors - my Asus board runs DC fans off or at least 60% and PWM starts from 20% (the AI Suite allows to turn them off too). They are easily interchangeable though. DC fans are better saved for the stock controller in the chassis as that just uses voltage (DC).
The bottom fan is easier to install if you do it before the PSU.
TBH, I would continue research and see if there are larger, more expensive and advanced cases available that are suitable for you. I'm sure that you could build with R5 but there might be some slight compromises necessary. It works very well for my system and my hardware tops at only 60-65C without overclocking, but you're likely to install about 150W more TDP than what I have currently running.
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