First of all: If you really want to be as fair and sustainable as possible and/or have the least (environmental, social) impact, I would argue that the best choice always is to get a second-hand phone. In this aspect, I would say, it’s even “better” than buying a new FP2, though there might be other aspects/reasons to buy an FP2 (e.g. to support Fairphone to increase visibility of the project and awareness about the subject -> to change the industry in the long run).
As (unfortunately) there are so much people out there switching their phones quite often, it shoud be fairly easy to find a second-hand phone (even a powerful with good specs if you need it).
If a second-hand phone is no option for you (for whatever reason), choosing the right phone (or company first) depends a lot on the criteria you apply. The site you cited has mostly “soft” or “passive” criteria about what the companies are engaging for (or not) or how transparent they are (e.g. to publish an environmental report is transparent, but it does not tell anything about how environmental-friendly the company actually is - this could also be (and is often enough) used as greenwashing; to have a code of conduct is nice, but tells nothing about the content and so on). I don’t want to downvote these criteria, but the main criteria you wanted to focus on are not included there and I am too missing those other criteria concerning the effects of their core business and production process, i.e. labour treatment, environmental impact of the production, origin of raw materials, repairability and longevity (hard- and software and support of these) of the end product and similar stuff.
There are also other sites with rankings of electronics companies (and there are surely even more I don’t know of (internet search might help)):
http://rankabrand.org/electronics and its Sustainable Electronics Report 2014
http://www.hightech-rating.ch/ (unfortunately only in German and French)
According to the first one, Huawei and LG are apparently rather bad choices. But I’ve not studied them in detail and don’t know their criteria either, so I can’t recommend anything. After a short skim, they seem to have quite some soft criteria as well (probably the report has more details). I don’t know how the greenpeace sites behave in this context.
Anyway, take a look at the links, if you like. If you do so, please report back what you’ve found out, because this might also be helpful to others!
@All: There may also be other useful sites out there concerning this subject? I’d also be really interested to see them. I guess, there are even forum topics about this I am not aware of.