As a new player, you should get 4 5* (rainbow) recruitment contracts very early on. This will let you get the most useful characters from the pub. Additional contracts will slowly trickle in through various events and passes.
Must Haves
Yes, even if you already acquired them through random draws, they're worth a +1. However, you can delay recruiting for upgrade purposes until later if you have a strong need for one of the other characters.
Liatris (Rodev's Star) - Ch8
One of the best DPS in the game
Ability does decent damage and has a strong DoT
Has strong synergy with her other costume, Maid Name R
Note that getting duplicates of this costume only improves the DoT. If you're winning on turn 1, this won't do anything for you. However, getting to +3 will reduce the SP cost, so keep that in mind for later.
Diana (Adventurer of Unknown) - Ch10
One of the best buffers in the game
"Dispatch" field ability brings in useful items, such as cooked rice or dia, once per day.
Buffs "property damage", which increases your character's damage when you have an elemental advantage
Levia (Night of Jealousy) - Random
Range is a 3 tile wide cross with exceptional damage on the main target and weak damage on the remaining targets
For most situations, her Track and Field Captain costume is preferred
Excellent against Partan (ch11 boss) or for Last Night
Venaka (Wind Dancer) - Random
Range is a 3x3 with the main target in the front row
Adds a vulnerability to wind debuff to the enemy (stacks additively with other vulnerability debuffs)
Highly Recommended
These costumes are very useful, but lower in priority than the previous group.
Celia (The Curse) - Random
"Absorb" field ability will grab all of the glitters (crafting materials & cooking ingredients) on the map for you, make sure to use Lathel's find ability first
High chain ability that's often used in end game content like Fiend Hunt (FH) to boost your main damage dealers' damage
Ideal if you have her other costumes as well
Olstein (The Fiend Scholar) - Ch4
If you already have him recruited (any costume), this costume falls into the "situationaly useful" category
"Dispatch" field ability brings in somewhat useful items once per day, mostly gold
Ability is a Skip 3x3 silence + SP recovery, which can be useful later in the game when you can't reliably clear fights in 1-2 turns. However, you're more likely to use Lucrezia, despite the smaller range, since her ability is cheaper.
Eleaneer (Piercing Magic Bow) - Random
Tied with Pool Party Schera (limited costume) for cheapest dispel, good in PvP if it's +3
Most accessible dispel after Schera, who becomes unavailable in ch13
As one of the few dark DPS, she'll be helpful against light enemies (chapters 10, 13, and 14)
Situationally Useful
Elise (Lovely Lady) - Random
Physical & magic defense reduction in combat
Note that this is only useful if the enemy has physical or magical defense
Unless you need her range, there's better options (Liberated Marauder Kry, Code Name A Rafina, B-Rank Manager Gray, DJ Venaka)
Notable Pushers
These costumes have abilities that are more than a simple push. Either more tiles or multiple targets.
Character
Location
Ability
Rou (White Cat)
Ch3
Teresse (Angel of Destruction)
Ch7
There are a few recruitables with unusual knockback directions. Refithea is worth getting if you also have the Pure White Blessing costume, but the others are low priority if you already have the character from a random draw.
Character
Location
Direction
Rubia (Thorn of the Desert)
Ch5
Very Front
Eclipse (The Dimension Witch)
Ch6
Skip
Angelica (Fallen)
Random
Very Front
Venaka (Wind Dancer)
Random
Very Front
Refithea (The Gluttonous)
Random
Skip
Notable Field Abilities
If you already have these characters, it's not a priority to recruit them for this purpose.
Character
Location
Ability
Description
Rubia
Ch5
Swiftness
Makes your dash gauge recharge 95% faster, useful for field challenges
Sylvia
Ch5
Bargan
Gives you a discount at the shop, does not work on ability pills (only useful if you want to do the cooking achievements)
Anastasia
Random
Dash
Faster version of Liatris's dash, but half the duration
Refithea
Random
Assemble
Grabs all of the Gluttis in the area, giving you a small amount of gold
Useful if you have the other costume(s), maybe
These costumes are either useless on their own or are eclipsed by the character's other costumes. They might be worth recruiting if you already have one of their other costumes. Listed by chapter order, then alphabetical.
Sylvia (Desert Flower) - Ch5
Anastasia (Gentle Maid) - Random
Helena (Top Idol) - Random
Rafina (Steel Engine) - Random
PvP Only
These costumes are generally not very useful outside of PvP (Mirror Wars). If all you care about is getting medals for purchasing the monthly costume from the shop, you can skip them. Doing well in PvP requires a significant investment, don't expect it to magically happen just because you recruit these characters.