I'll tell you what their special ability is and how good of a character they are. Basically tell you what characters you should put effort into training and which you shouldn't.
Blue Gem Characters:
First Doctor - Cures Stun, Unlocks all gems. I can't wait to get him because in series 5 (or in the doctor pack currently in the game's store) because of his incredibly useful special abilities. Looks like I have a new replacement for the 11th doctor, I'd definitely recommend.
11th Doctor - Does damage to all enemies. Being the only blue gem colored doctor, He's a great fit for any team stacked with blue gem characters. He does good damage and has a good special ability as well.
Adipose - Converts red gems to blue. Has some-what high health but average attack, I would not recommend because there are better options available.
Angie Maitland - Converts yellow gems to pink. Terrible stats, Don't bother wasting your time on her..
Bitey The Cybermat - Converts blue gems to pink. Similar situation to Angie Maitland, Not really worth wasting your time on.
Captain Rory Williams - Increases damage from blue gems attacks. This version of Rory has very high attack and would be a nice addition to any blue gem team.
Dorium Maldovar - Heal allies. Dorium is my official tank for my blue gem team and I would definitely recommend using him because there really are no other tanks for blue gem characters.
Queen Nefertiti - Heals allies. Pathetic stats, Don't bother.
Sam Garner - Converts green gems to blue. Read what I said about Angie Maitland, Same applies here..
Spoonhead 11th Doctor - Converts red gems to blue. The most well rounded blue gem character due to his high health and attack. A must have character.
11th Doctor Flesh Clone - Converts green gems to blue. Worth checking out because of his converting ability and he is not a bad tank option either. Dorium is prefer but he's worth leveling up if you feel the need to have the only quality gem converter of this color on your team.
Red Gem Characters:
War Doctor - Deals percentage of enemies' health in damage, Stuns all enemies. I love using 10th Doctor, He is a great healer, but it's gonna be tough to pass up on War Doctor due to the fact that he has great special abilities and John Hurt, who portrays the character, is a total bad-a$$
10th Doctor - Heals allies. Great to have due to his epic healing ability..
Adipose - Converts green gems to blue. What I said about the first one applies to this one.
Church Cleric - Heals allies. Average stats, Not worth wasting your time on.
Clara Oswald - Heals Allies. Clara is a great tank character due to her high health and is one of many must have red gem characters.
Fan Ood Sigma - Increases damage from red gem attacks. Not as good as a tank as Clara but his ability to increases damage makes him worth checking out.
Jennifer Lucas - Converts red gems to pink. Stats wise, She is not bad, but I don't see when I'd use her on my team. Not a bad character though.
Jenny Flint - Converts blue gems to red. Not a bad starter character but the moment you get River and Clara, Drop her. Her stats are not good and she little use outside of mid-season 7.
Martha Jones - Increases heal from pink gems. Terrible stats, Don't bother.
River Song - Converts blue gems to red. Like Clara, She is a great tank character and worth having.
Rory The Handbot - Increases damage from red gem attacks. Bad stats, Don't bother.
Special Agent Amy Pond - Stuns single enemy. Amy has very high attack and is a must have on any red gem team, Especially when pretty much every other red gem character has poor attack stats.
Strax - Heals allies. Don't even bother, He is awful stats wise..
Winston Churchill - Converts blue gems to red. A great tank option but with River and Clara already there and all three are pretty much exactly the same stat wise, Is he really needed?
Green Gem Characters:
Seventh Doctor - Deals damage to target enemy. I actually can't wait for another green gem colored doctor because I do not like him at all.
Adipose - Copy and paste what I said about the other two here.
Artie Maitland - Converts green gems to pink. Average stats, Would not recommend..
Captain Henry Avery - Converts green gems to pink. Slightly better health than Artie but still would not recommend.
Church Verger - Increases damage from green gem attacks. His high health makes him a worthy tank on your green gem team.
Craig Owens - Deals damage to all enemies. His high attack makes him one of few green gem characters worth leveling up.
Fan Churchill - Increases damage from green gem attacks. What I said about Church Verger applies here as well.
Lorna Bucket - Deals damage to all enemies. Another high attack companion well worth having on your team.
Punishment Media - Cures Poison. Don't waste your time on this one.
Rory Williams - Heal allies. Once again don't bother wasting your time.
The Girl Who Waited - Deals damage to all enemies. Solid health but still not worth leveling up.
UNIT Medic - Converts blue gems to green. Terrible stats so don't bother.
UNIT Soldier - Poisons enemy for x amount of turns. Above average in both health and attack but there are far better options available in my opinion.
Yellow Gem Characters:
Third Doctor - Does 20% of overall health in damage to enemies, Turns weeping angel stones into pink gems. Does better damage than the Sixth Doctor and has better special abilities so he should be the leader of your yellow gem team.
Sixth Doctor - Poisons target enemy. Read what I said about the third doctor.
Adipose - Read what I said about the others.
Alex Thompson - Converts black gems to pink. Don't bother with him.
Amy Pond - Increases damage from yellow gem attacks. Average stats, I wouldn't recommend.
Brian Williams - Increases damage from yellow gem attacks. Really the only yellow gem tank available and with his solid special ability, He's certainly worth checking out.
Canton Delaware III - Deals damage to all enemies. Brian is the better tank but Delaware isn't a bad second option, All depends on the special ability you want.
Church Bishop - Deals damage to all enemies. His high attack makes him worth leveling up.
Handles - Converts black gems to yellow. A great tank option with a great special ability, Handles is a must have on all yellow gem teams.
Jack Harkness - Cures stun. A great tank with solid attack and the only character with the ability to cure stun. Once again, He is a must have.
Madame Vastra - Deals damage to all enemies. Great well rounded character who I have used since I first started the game and I still do. Highly recommended.
Ood - Increases damage from yellow gem attacks. A good tank option but sadly only rarely available in stores..
Old Canton Delaware III - Heals allies. Average stats, Don't bother.
Punishment Soldier - Deals damage to all enemies. Don't bother wasting your time.
Sarah Jane Smith - Deals damage to all enemies. Once again, Don't bother.
Black Gem Characters:
Eight Doctor - Heals allies, Cures poison. Sadly he is the only black gem doctor, I plan on switching him out once a new one comes along.
Ninth Doctor - Increases heal from Pink games, Heals 30% of your max HP. Ninth is a must have on your black gem team due to his great special abilities.
Adipose - Read what I said about the others.
Dr. Edwin Bracewell - Sets a bomb and deals damage to single enemy. A good tank option worth leveling up..
George Thompson - Stuns enemy. His very high attack makes him a must have..
John Riddell - Stuns enemy. Another great tank option worth leveling up..
K9 - Stuns enemy. His stats are slightly lower than George's but if you like him as a character, He isn't that bad.
Malohkeh - Cures poison. Don't bother.
Miranda Cleaves - Deals damage to all enemies. A nice well rounded character but due to the tank and attack options I listed above, You could pass on her because she isn't a top priority.
Oswin Oswald - Increases damage from (red, blue, and green) gem attacks (changes each rank up). Stats are on par with Bracewell and Riddell but the useless special ability sort of kills this character for me.
Porridge - Sets a bomb and deals damage to target enemy. Not bad to start off with and his stats are once again on par with Bracewell and Riddell so he's not really needed. It just comes down to preference.
Stormageddon - Converts yellow gems to black. Useful special ability but his stats are not that good. Think hard about this one.
UNIT Commander - Increases damage from black gem attacks. Poor stats so don't bother.