I should technically solder more of this, as it's mostly together with prototype cables at the moment. Any soldering iron should work, but I am partial to Weller Soldering Stations. I have one from ~10 years ago that has an analog adjustment, though now I see they look to be mostly digital. Their website has them around $300 for some reason but they are on amazon for closer to $100 (which is what I got mine for).

https://www.weller-tools.com/we1010na/