I am not a lawyer, and I am not your lawyer. This answer is intended as legal education, not legal advice: I am trying to explain the situation as well as I can based on my own (untrained) understanding. If you have any questions, doubts, or concerns about how your planned actions square with any of this, you need to get your own lawyer to answer them.
- How should I proceed if I'm interested in taking those elements of such SRDs?
The material on those sites should all be Open Game Content, that is, content released under the Open Game License. You can use them under that license, but you have to understand the license and how to use it. You don’t need a lawyer for this, if you are very careful and do the research, but if you’re serious about this it might be very worthwhile to get actual legal advice from your own lawyer on how to work with the license. But for what it’s worth, none of the companies I’ve worked with that have published things incorporating Open Game Content has actually used a lawyer, and none of them have been sued.
- Would it be wiser to take some of those elements as inspiration to make my own version of those values (environment and organization)? If so, would I still have to make some legal move?
OK, so first, there’s the legal theory. “Derivative works” are still (usually) covered by copyright, which means if you make something derivative of copyrighted content, the holder of the original copyright has some rights to your work (namely, they can prevent you from distributing it, though you retain the right to prevent them from publishing your derived work—basically, in that case, no one wins and the material has to stay in a drawer somewhere). Whether or not something is “derivative” or not can get extremely contentious, and you will almost-certainly need professional legal advice on whether or not your work would be considered derivative.
But, theory aside, practically speaking, remember that ultimately, no one can truly decide these matters except for a court. If Wizards of the Coast or Paizo believes your work is derivative of theirs and they have copyrights over it, they can sue you. You could defend yourself, and the burden of proof would be on them to show that it was in fact a derivative work, but the cost of the defense would likely be immense and probably not realistic as a small start-up, much less an individual. Unfortunately, that means that to be safe, you are better off just staying far, far away—even if you get a lawyer to look into things, they will most likely wind up just telling you that whether or not you’re technically right here is a moot point since you won’t be able to afford the defense. No lawyer can promise you that you won’t be sued.
Licensing the material under the Open Game License eliminates those concerns, since you are allowed to use it—as is or as part of a derivative work—when you agree to the license. That’s kind of the point of the Open Game License: to avoid the toxic risks that copyright law burden you with and to give you a safe way of using these things. It’s still not 100%–they could sue you claiming that you violated the license somehow—but it makes it vastly less likely.
- Would it be wiser to just take from one SRD?
It won’t matter, but pay careful attention to the attribution requirements in Section 15 of the Open Game License—that requires you to list every OGL source you use for your material, as well as all the sources those sources list in their own Section 15. It gets very large, very fast, and can be a moderate pain to deal with.
Also, for the most part, you aren’t taking from the SRDs themselves, certainly not from those websites. You’re taking from the original publications that were released under the OGL. The SRD sites should list where things came from; you have to follow the trail back to the original and list that in Section 15.
- Is it safe to take Open Gaming Network websites as part of the SRDs?
It should be, but again, you have to follow their links or citations back to the original source published under the Open Game License, and cite that. You can’t just cite the website you got it from, you have to go the original. And if the site got something wrong—rare, but not unheard of—you need to know that, because “oh, it was on this Open Gaming Network site so I thought it was Open Game Content” isn’t going to fly. You have to check.