Betta fish question?????

So I plan on getting a Betta fish soon. I've had Betta fish before, and I want to know the best way to keep it living. I had one betta that lived for four years, but my last one only lasted a couple months. I noticed something happened to his finn and he could no longer get to the surface to get his food, i tried to push it down for him, but he wouldn't eat it and soon died. It was a filter tank with only the stones on the bottom, and a little fish cave, do you have any idea how his finn could've gotton hurt? Also, he once stayed perfectly still for three days. I was sure he was dead. I know this is bad, but I just did it to make sure he was alive, I shook the tank slightly and he still didn't move. I put food in and he still didn't move! Finally three days later he just started swimming again? Do you think he was sick? Is there anything I can do to prevent my new fish from getting sick? Is there any way to tell apart a healthy fish from a sick fish in the store when I pick it out? All answers are greatly appreciated! Also I either wanna name it Vanessa or Gia, which do you like better? thanks!