The Hero Hunters Best Characters are going to be the ones that have the most stars and will take provably the longest to unlock. The highest star level that a hero goes up to seems to be 7 at the moment even though it looks like they have a limit of 10. The developers must have more content that might be available in the near future.
You can check the stats of heroes before you get them so you can have an idea of what your looking at. You are going to need at least one for every type of attack and you going to wont ones with the highest attack power. To get more attack power your going to have to get better quality heroes as star count will have a direct relation to power levels.
One of the best places to get heroes is opening chest in the store using gold. Though this can get kind of expensive and can be a long time between draws you can usually get someone the has good enough stats. The odds of getting a really high quality character are probably pretty slim as the developers are trying to make money so they turn the odds way down.
After you have a Team level of 10 or higher you are able to partake in missions that will allow you to earn fragments so you can gain new party members. Unfortunately, the ones you wont the most are going to be the hardest to get and longest to acquire.
If your interested in more related information you can check out the Hero Hunters Wiki.