The Captain is extremely similar to the Chapter Master, lacking 1 wound, 1 attack, and Orbital Bombardment. He’s a bit less durable and does a bit less damage, but he otherwise can be armed and used identically to a Chapter Master. For reasons lost in the void that is GW rules design, the Terminator Captain is a separate entry rather than an upgrade to the standard Captain, but none of his rules change.
The Librarian is the budget HQ choice for Space Marines. His statline is intermediate between a Captain and a Veteran Sergeant, so he won’t be doing much damage on his own and he’s extremely easy to kill. If you want to keep him safe, your only real option is Terminator Armor with a storm shield. He comes with a force weapon of your choice, making him a wild card against enemy characters and monstrous creatures. Beyond that, he doesn’t really need any extra equipment. However, it is almost always worth paying the points to make him a Mastery Level 2 psyker, if only for an extra psychic power.
I’ve gone back and forth on how to use the Librarian. He has access to every psychic discipline except Divination, and I have leaned toward Telepathy as it seems useful in a large number of circumstances. However, psykers have trouble being in transports, and that’s how I’ve run mine so far (I’ve also discovered this with my Eldar). When he’s riding in a Rhino, Blessings and Maledictions can only be cast on his unit or the Rhino, greatly limiting their worth. When he gets out, he can’t cast them until the next turn, so he generally won’t be utilizing his psychic might until turn 3. I generally rely on him to cast a Witchfire power (Psychic Scream seems the best of the Primaris options) to augment the firepower of his squad when they disembark. The results have been underwhelming so far, and he tends to die shortly afterward.
These problems could be mitigated if he weren’t in a Rhino, freeing him up to cast every turn. The majority of powers seem to have short ranges, and he lack access to the buffs from Divination, making him a relatively poor choice on foot as a backline caster. However, I could see him advancing with a Centurion squad and providing them with some psychic support. Like the Chapter Master, I think the Librarian is best off on a bike, allowing him to cast with impunity and get within range of his powers.
One reason that I feel like the Librarian isn’t working as well as I would like is that I generally haven’t run large, pivotal Death Star style units. Librarians work well with these units for two reasons. First, the unit is tough enough to keep the Librarian safe. Second, the unit is important enough to really benefit from any buffs that the Librarian generates. Making a Death Star Invisible is way more useful than casting it on a Tactical squad (or even the Sternguard that I usually run him with). If you plan on running this type of unit, definitely consider taking a Librarian to supplement both its offense and defense.
Or do what everyone else does and just take Tigurius.
The Chaplain shares the Librarians intermediate statline, but comes standard with a power maul and a 4+ invulnerable save. He’s also a Zealot, so he conveys Fearless and Hatred to any unit he joins. His options are very limited, but he can take a power fist because GW makes one model armed that way. I actually really like arming the Chaplain that way, as it allows him to either swing at initiative with AP4 or go last with AP2, which is very handy for an assault character. Even so, I usually take the cheap option and just leave him with his Crozius Arcanum. You’re taking a Chaplain to give Zealot to an assault unit.
Because he’s such a support character, the way you equip a Chaplain is dependent on on what squad you are pairing him with. If you want to make your Assault squad hit harder, he’ll need a jump pack. If he’ll be riding in a Land Raider, he can be made more durable with Terminator armor. I particularly like the idea of putting him with a bike mounted Command Squad. It’s one of our better assault units, and it’s greatly benefit from being Fearless. When you put that many points into a squad, you can’t trust LD 10, and the re-rolls to hit don’t hurt either.
Taking a Captain, Librarian, or Chaplain, as well as any of their named character counterparts, allows you to take a Command Squad. While the Honor Guard is a very well-equipped assault unit with relatively few options, the Command Squad is one of the most flexibly equipped units in the game. They are stuck at five members, but every member can be equipped with any melee or special weapon that they want, as well as budget priced storm shields. They also have the option to take bikes, greatly adding to their speed and durability.
You can upgrade members of the Command Squad to specialists, the most important of which is the Apothecary. He doesn’t cost much to give the squad Feel No Pain, and it is absolutely worth it on such a well equipped squad. You’ll also likely be running independent characters with the Command Squad, so they’ll benefit from Feel No Pain as well. The Company Champion is also a nice upgrade, getting a power weapon, combat shield, and an extra point of WS for the same cost as a normal power weapon. The downside is that he must issue and accept challenges, but he’s not enough of an investment for this to be a massive problem. Finally, you can add a Standard Bearer with a Company Standard or Standard of the Emperor Ascendant, but neither of these are as efficient and useful as the Chapter Banner that Honor Guard can take, so I would skip them in most circumstances.
With all of the options Command squads can take, it can be a bit overwhelming to equip one. I think the key is to design them for a specific role, generally either firepower or assault. A firepower squad will usually take the maximum amount of a special weapon, as well as a transport to allow them to get into range to use them. Drop Pods pair well with maxed out plasma guns, flamers, or meltaguns, depending on what targets your army has problems with. Grav guns work exceptionally well with Command Squads on bikes, as they are Relentless and can fire their full number of shots on the move. Assault oriented Command squads really need bikes, as no other transport is as efficient at reaching combat. Beyond that, they should take storm shields and an assortment of power weapons and fists. Both types of squad benefit from an Apothecary to keep the alive and functional a bit longer, though Feel No Pain is even better on a bike squad because bikes raise their Instant Death threshold and make Feel No Pain apply to almost all wounds.