The obvious goal is to make the strongest, most successful team. There are several "types" of members that you can expect to have. These can be either focused on different areas of expertise, or can be theme characters (which are just fun to use).

There are really two different schools of thought on this. Some people believe that it is better to have all of the monsters on a team with both healing and offensive spells. To some extent, this is true. In crucial battles, it is necessary to have everyone with a healing spell, and some kind of offense. I am offering an alternative strategy to that.

The members I have listed below are different types which can be mixed and matched to get different teams (with different strengths and weaknesses). I will talk more about this later. Below each member, I have listed a few monster types that would be ideal for this type of character. Keep in mind that the members of the Boss family will work for any of these, and are a powerful addition to any team.

1. The Healer

This member should have all the best healing spells, evolved to either HealAll or HealUsAll (from Heal and Heal Us, respectively). This monster will also have some kind of spell to bring back the dead, like Revive. It will also need something to get rid of status ailments, such as surge (to cover everything). Lastly, you can't be just defensive, so you need one or two heavy hitter like BigBang, MultiCut, or HellBlast (don't get rid of all your MP by using MegaMagic if that monster is to be your main healer) or even a GigaSlash (good for taking out one big nuisance)

2. The Handyman

This member is just helping everyone on all fronts. He will be equipped with a healing spell, and maybe a revive. The main thing will be a bunch of increasers, like SpeedUp or TwinHit. These will improve everyones attacks. Also, he should have some good attacks of his own. A good person to have megamagic, because after he builds up everyone, he can unload what he has left. Would be nice to have gigaslash too.

3. The Overkill

Well, for those that don't really care about a finesse win, they just need someone that can quickly dish it out. This person should have all the awesome attack spells (BigBang, Multicut, MegaMagic, GigaSlash, HellBlast). Also, a good physical attack such as QuadHits would be useful too. Any supplemental attack spells would be good.

4. The Dragon

One of the theme characters. This character will have almost all of the breath based attacks (BlazeMost, PalsyAir, SleepAir, PoisonAir, WhiteAir, White Fire) as well as BeDragon. In addition, this dragon character will have SuckAir, to increase breath attack effectiveness. Like most theme characters, this monster will have StopSpell (or even DanceShut or ThickFog)to prevent any offense other than the big bad breath. Though for any theme character, it is good to keep like 1 or 2 spots open for an offensive (Bigbang, Multicut, GigaSlash) or defensive (HealAll or HealUsAll) skill, since the opponents may have a counter for your specialty.

5. The Dancer

Another interesting theme character. This character will have all of the dance attacks (K.O. Dance, LifeDance, RobDance, PaniDance) and some spell stopping attacks (StopSpell, ThickFog, or MouthShut). I would include some theme style attacks, like HighJump, SideStep, or BigTrip. Again, for any theme character, it is good to keep like 1 or 2 spots open for an offensive (BigBang, Multicut, GigaSlash) or defensive (Healall or HealUsAll) skill, since the opponents may have a counter for your specialty.

6. The Caller

Since there are not that many different Call skills that this member would have, this class ends up being a modified HandyMan. The Call skills are YellHelp and whatever "evolution" of TatsuCall (Bazoo, Samsi, Diago) you have. Good person to have MegaMagic (to unload after doing its initial TatsuCall and maybe a few YellHelps)

7. The Hitman

This guy is ready to lay the smack down on anything he encounters. This member will have maybe 6 or 7 of the 10 family cut attacks. By narrowing down the number of these he is using, he can keep a bunch of attack up attacks like TwinHit or Chargup, or Berserker. To go with the theme, may want a Gigaslash or Defeat.

8. The Nullifier

This monster will be there to essentially neutralize the enemy party. The specialty of this class is to remove spell, breath, and dance ability, and make their physical attacks useless (making them sitting ducks). The main skill nullifiers are StopSpell, MouthShut, and DanceShut. To get rid of physical attacks, there is Radiant and SandStorm. To lower their stats, there is Curse (which does random things to them), Defense and SlowAll. And to just keep them from doing ANYTHING, there is BigTrip and WarCry. Another good person to have MegaMagic, since they can unload once the enemy is neutralized.

9. The Elemental Master

These monster will take 1 or 2 of the elements and will pool various attacks from them. The reason for this, is that there is usually at least one or two resistance groups that monster families are weak to (besides the MegaMagic and GigaSlash ones), and it might be helpful to have these available. The FAQ by Alex Jackson breaks down the resistances into several main groups. Pick 1 or 2 groups, and then flesh out the skills with enhancers (like for breath attacks).

Remember that after a lot of breeding, most of your final monsters will max out their stats (or get really close), and so the stats really won't become the deciding factor in what class that monster should be. It then becomes a matter of preference.

Team Selection

Now that you have seen some of the different types of members, I will outline what different teams can be made from combinations of these members.

There are really infinite combinations, each which could work given the right planning and strategy. I will add more as this type of strategy becomes more widespread.

Team 1 - The Castle

• Monster 1 - The Healer
• Monster 2 - The Overkill
• Monster 3 - The Hitman

  I call this the castle, because it always reminds me of the 
  relationship between wizard (healer), knight (overkill), and archer 
  (hitman) in the castle siege of any good medieval legend. 2 offensive, 
  one good defense to back them up. This is probably the most common 
  team combination, at any point in the game.

Team 2 - The Circus

• Monster 1 - The Dancer
• Monster 2 - The Caller
• Monster 3 - The Nullifier

  I call this a circus because it represents the grouping of a bunch of 
  weird skills. The Nullifier here will block the enemy, allowing the use 
  of odd skills. The Caller will probably go in for the most damage with 
  the MegaMagic. A hard team to play (though very entertaining). Something 
  nice to tinker with late in the game.

Team 3 - Circle the Wagons

• Monster 1 - The Healer
• Monster 2 - The HandyMan
• Monster 3 - The Hitman/The Overkill

  Representing the obviously defensive posture of "circling the wagons", 
  this team relies on the offensive power of the Hitman/Overkill to win. 
  Although not a good team to use late in the game, this formation is 
  handy when starting out early in the game with one REALLY good monster 
  and a few mediocre ones. 

Team 4 - Tag Team

• Monster 1 - The Healer
• Monster 2 - The Overkill
• Monster 3 - The Dragon

  Two great offensive powers, protected by a trusted Healer. Very strong 
  late in the game. 

Team 5 - Earth, Wind, and Fire

• Monster 1 - Ice and Wind Master
• Monster 2 - Fire Master
• Monster 3 - The Hitman

  This team relies on the fact that the two elemental masters will be 
  able to really whack most enemies. The Metal Slime sub-family will be 
  taken out first by the Hitman, so no need to worry about those.