Having three characters can be overwhelming, especially when it come down to all the different races, classes and strategies. So how do you choose?
This guide's to help you decide.
What is a Party character? And what can they do?
A Non-Player-Party character (or an NPPC) is an AI controlled character who will, usually, accompany you on your adventures. They will fight enemies, try to pick up items, guard positions, and they will do their best to avoid enemies - unless they're melee characters, in which case they'll merrily charge headlong into them, merrily swinging their swords like a lemon. You may freely select which character you control, access their inventory without controlling them, ask them to wander or hold position.
Unlike yourself, NPPCs are immune to projectiles, and will, if selected to follow you, teleport to your location if they are too far away, and appear to be immune to fall damage. Oh, and they have unlimited mana. When an NPPC dies, they will respawn a short time later, and then teleport to your location normally. They will leave a headstone, they will lose money (I don't recommend using Hardcore or Mediumcore NPPCs), and they will lose Experience.
Knowing how your NPPCs will react is important. For example, if you're flying upwards to evade a boss that's following you from below, note that your hapless NPPCs will repeatedly teleport to your location, fall down, hit the boss, take damage, fall too far away from you, and repeat the process until they die. If you're planning to face a boss, consider putting them in Guard mode at the sides of your arena, then let them fire from the comparative safety of a platform, ignoring projectiles and hopefully not getting themselves killed by other means.
Quirks and Pitfalls
NPPCs will attempt to use every skill they have. They will always use the best summoning weapon in their inventory until they can't summon anymore. They will always use the first weapon in their hotbar. They will always use mounts and pets. They will also spend money whenever you're near an NPC to "refill" their ammo. Note that this applies even if they don't use a ranged weapon. Money is pretty worthless in N Terraria, but keep it in mind. Finally, if they have a melee damage type weapon equipped, they will try to approach their targets. They also have trouble understanding that lava/water hurt them.
So, if you'd rather thay not start gallivanting around on a mobile bee, wasting damage opportunities with their useless baby slimes and ramming their faces into boss enemies, then make sure their "equipped" weapon is a ranged or magic weapon that matches what skills they have, that their only pet is one that boosts their relevant stats, and that they don't have a mount (since NPPCs will have enough trouble following you down through a hole without one). If possible, do make sure your allies are geared up with Magma Thunders and Wings if you are, since they'll quite probably wander into lava and get stuck without the right mobility items.
Which classes do what?
You can, hopefully, keep your two mildly suicidal friends alive, so now the second consideration is to pick NPPCs who will actually be helpful.
Melee AI Sucks: Sad but true, even if they're wielding the Terra Blade, they will charge directly at the enemy, typically trying to reach the middle of that enemy. If you're planning to have someone who uses melee weapons, have it be your main character. And yes, this does apply to Vampire Knives and Paladin's Hammer users. This rather discounts Thief and Fighter as NPPCs, though they're great potential picks for a main character thanks to skills the AI won't utilise correctly.
Acolyte: Heal, buffs, and a great choice for Spectre Armour with their boosted magic damage, which will top off anything that Heal misses. Since mana isn't an issue, and neither is cast time, 130 Intelligence, 130 Charisma Acolyte will brutalise everything with summons, wreck everything with massive damage magic weapons (Razorpine, for example), and heal for massive amounts of damage. It's up to you if you want them to wear Spooky Armour for even more summon damage, or Spectre Armour for better magic damage, but either way they'll be making you feel ashamed of how mediocre you are in comparison.
Mage: Their immunity to projectiles and general tedium of crawling along at snail's pace makes the mage a nice choice for an NPPC, since they'll have the time to be charging and firin' their lazors.
Merchant: Permanent Scavenger's Eye effect. This is about all that having a Merchant in your group will really offer. If you want one, consider maxing out their charisma and vitality, give them a shield and letting them summon up an army to fight while they sit around blocking and spotting ore for you.
Ranger: Stand around and shoot. The Ranger is a nice choice for bosses, since you can set them to Guard and they'll generally stay put, for the most part, letting them maximise the benefits of Shroomite gear. I tend to be a bit of a snob against Ranged damage though, and they don't offer any of the other skills you might enjoy from other character.
Super Terrarian: They'll drive you nuts by spamming their unupgraded Magic Missile, trying and failing to use their Heavy Slash, and generally being annoying flying bands of text, but a ranged damage Super Terrarian (if you're going magic, go with a mage or acolyte) can perform about as well as a Ranger while dying less and healing you more.
Tank: A tank can be either great or bad, depending on the enemy. A high level tank (5000+ defense) will take 1-500 damage (500 isn't serious damage when you have 10 000+ health) from almost all of the game's enemies. With beetle or turtle armor, enemies will attack the NPPC while you can lay back and shoot the enemies from far and safe if you're a mage or a ranger. Some may prefer to be a tank itself taking all the damage while your NPPC's shoot the enemies. A tank can do notable damage too if you go 130 vitality and 130 strength, but if you want a pure tank, agility would be a better choice than strength for the dodge and speed bonus for extra survivability.
So, if you don't care about redundancy, Acolytes should probably suffice for your Magical needs, while Super Terrarians should do the job for Ranged damage, both healing you, dealing out copious amounts of damage, and not running headlong into lava and/or boss enemies. If you're not playing a Super Terrarian yourself, then having one in your party will let you enjoy the permanent Scavenger's Eye and the permanent Acolyte buffs, supplying every worthwhile buff skill to you.