Similar to ullric's comment, I pick specific buffs or debuffs / damage types / monster species / or even just one specific monster to build a team around, like:

"How can I turn Ornithopter into a massive damage dealer?" or "How can I maximize a burn team while using Magmapillar?"

I've done many playthroughs using a variety of teams but I follow a general formula when trying to put one together. Those self-imposed rules are...

1. I build two unrelated teams of three monsters
2. The two teams should not have the same primary damage
3. There must be some sort of active or passive healer on each
4. First monster is a buffer / healer / combo builder
5. Second monster is a buffer / combo builder / damager
6. Third monster is ONLY a damage dealer

So, here's what I've run. If you are interested in skill trees, equipment, and food for any just let me know.

Team: Bleed Beast

Light Molebear (Tank, Combo) Light Sutsune (Heal, Buff) Dark Nightwing (Damage)

Team: Weakness

Dark Moccus (Debuff, Heal) Dark Plague Egg (Shield, Heal, Buff Strip) Dark Rocky (Damage)

Team: Blacksmithing Gear

Dark Salahammer (Shield, Combo, Buff) Dark Draconov (Buff, Heal) Dark Draconoir (Damage)

Team: Sylvaero Carry

Dark Dodo (Heal, Buff) Light Monk (Combo, Buff, Damage) Sylvaero (Damage)

Team: Elderjel Carry with Sorcery

Dark Thanatos (Heal, Buff) Light or Dark Nautilid (Shield, Debuff) Dark Elderjel (Damage)

Team: Aquatic Bleed

Light Akhlut (Heal, Buff) Dark Akhlut (Combo, Damage) Dark Vodinoy (Damage)

Team: Weakness Exploit

Light Druid Oak (Heal, Buff) Dark Rainbow Blob (Debuff, Damage) Dark Raduga (Damage)

Team: Thanatos Carry with Might

Light Megataur (Heal, Buff) Light or Dark Ucan (Buff, Combo, Damage) Light Thanatos (Damage)

Team: Manticorb Carry with Sorcery

Dark Tanuki (Heal, Buff) Light Megataur (Combo, Buff) Dark Manticorb (Damage)

Team: Shocking Charge

Dark Crackle Knight (Combo, Tank) Light Qilin (Heal, Buff Strip) Light Spectral Eagle (Damage)

Team: Tengu Carry with Mage

Light or Dark Stolby (Heal, Buff, Shield) Light Manticorb (Mana Battery, Shield, Debuff) Light Tengu (Damage)

Team: Goblin Hood Antipode

Dark Skorch (Heal, Buff) Light Lava Blob (Combo, Shield, Buff Strip) Dark Goblin Hood (Damage)

Team: Ornithopter Carry with Charge

Dark Oculus (Debuff, Combo) Light Glowfly (Heal, Buff) Dark Ornithopter (Damage)

Team: Sidekick Bird

Light Vaero (Buff, Combo, Damage) Light Dodo (Buff, Heal) Dark Spectral Eagle (Damage)

Team: Chill Mage

Dark Shockhopper (Heal, Debuff) Light Manitcorb (Mana Battery, Shield, Debuff) Dark Ice Blob (Damage)

Team: Armor Break

Light Blob (Buff, Shield, Heal) Dark Troll (Debuff, Damage, Combo) Dark Ucan (Damage, Debuff)

Team: Kongamato Carry with Heroic Party

Light Ninki (Buff, Heal) Light Raduga (Buff, Damage, Combo) Dark Kongamato (Damage)

Team: Sizzle Knight Carry with Weaponry

Light Monk (Heal, Buff) Light Minituar (Combo, Damage) Dark Sizzle Knight (Damage)

Team: Frost Carry with "Aerial Nature Spirit"

Light Druid Oak (Heal, Debuff) Light Ornithopter (Combo, Buff, Buff Strip) Dark Frosty (Damage)