As far as flexibility goes, do you have a history with either carpal tunnel or arthritis? If so, you definitely don't want to push your hands past their pain point. Accuracy in signing is important, but not worth hurting yourself over. There are many ways to make your signs more relaxed so that they come close enough to the correct handshapes to be understood, even if they don't match quite perfectly. It would be similar to having slurred speech or a speech impediment, but having unclear words is still better than no words.
If you don't have a medical issue, and your hands simply aren't flexible, it might be worth doing some hand exercises to strengthen their muscles and flexibility. A (very light tension) grip strengthener such as this one might help:
https://www.amazon.com/GRIP-MASTER-Gripmaster-Hand-Exerciser/dp/B0006GBDZY/ref=sr_1_2?keywords=gripmaster&qid=1553989655&s=sporting-goods&sr=1-2
Alternating squeezing all fingers at once and then releasing, and then doing the same with each finger on its own, for 1 minute, then taking a 1 minute break, then repeating the process. Doing that for 10 minutes a day in each hand will strengthen their muscles gradually over the next few weeks, and you should find your ability to close your fingers becoming easier.
For stretching your fingers, I would find a strong rubber band and do similar exercises by putting the band around all your fingertips (or just your thumb and one finger), and stretching them apart. Doing so would gradually increase your flexibility.
Just like any exercise, you don't want to overdo it, and if your hands go beyond simple "stress/soreness" while doing it, and start getting into "pain," you should stop immediately and reduce the tension or amount of exercise.
------
As for online resources, you will find different things in each one, but the site that I usually recommend for lessons is Lifeprint.com, and the youtube channel of its teacher: Bill Vicars. The website includes culture lessons and examples of how things vary from person to person, which will help to understand why you've seen so many different things so far.
Feel free to provide more info or ask more questions if needed!