F4LL0UT: Thanks for your replies. I skimmed through the posts here before going to the electronics store that I usually use (Komputronik, for anyone wondering). That particular one had only four different models available, only two of which had enough wattage, and I just wanted to get it over with so I ultimately didn't really have much of a choice. One was some cheaper 550W PSU from Corsair, the other one a rather pricey 600W PSU from be quiet!. I really just wanted to be on the safe side and and went with the 600W one, just for the sake of being at least somewhat above what is the recommended minimum for my graphics card, especially taking into account that I have more components inside my PC than the average user and may upgrade yet again in the near future (although it turns out that the power usage of the 10xx series seems to be lower than for my particular card).
Anyway, so I ended up getting a Pure Power 10 from be quiet!. The user reviews that I've seen online were very positive, it is indeed quiet and it's modular so so it was super easy to connect and there's not much of a mess in my PC now. In the process of installing it I almost broke my PC but everything's fine now. I finished another mission in Company of Heroes 2 on highest settings (which was impossible with the old PSU) and did not run into any issues so I guess mission accomplished.
Thanks again for your advice, folks!
Edit: Oh yeah, and I chose tburger's answer as the solution because going modular is pretty much the best lesson I've learned here. :D