Ultramarines are really spoiled for choice when it comes to special characters. They've got more on the main rulebook than any other Chapter, and the Badab War characters add even more. I'll just be covering those in the main book here, with the Badab characters getting their own post.
Marneus Calgar is the Chapter Master of the Ultramarines, and is every inch the tank that Lysander is. With the Chapter Master statline, Eternal Warrior, an iron halo, and either artificer armor or terminator armor, Calgar is extremely durable. He wears a pair of power fists with an AP2 storm bolter, so his damage output is very respectable. Due to his Titanic Might rule, he re-rolls and failed Armor Penetration rolls, so he’s even more reliable against vehicles.
For all of his personal abilities, you’ll probably take Marneus because of his army support abilities. His God of War rule has two massive effects. First, all Ultramarines in his army can choose to pass or fail any morale check. This is terrifically useful, as it makes your army completely reliable. Your units will never fall back off an objective or off the table. If they’re in an assault they don’t want to be in, they can always try to get out with no repercussions if they fail. Beyond this, it also allows your army to use one of the Combat Tactics twice each game. This will usually be the Tactical Doctrine, as it has the most uses, but you can choose the others if circumstances demand. Between these two abilities, Calgar gives you an army of Uber-Ultramarines.
Marneus Calgar also doesn’t have a fixed Warlord Trait. He rolls three times on the Space Marine Table (there’s some argument about whether he can use the base Warlord Tables), and you get to choose one of the results. This gives you a much better chance to actually get something he can use.
Calgar is everything you want from a Chapter Master, and he adds a tremendous amount of reliability and flexibility to your army. Despite his high points cost, I think you need to seriously consider Calgar if you’re running Ultramarines Chapter Tactics. His only option is to replace his artificer armor with terminator armor that allows him to sweeping advance and includes a teleport homer. It costs a few points, but doesn’t really change much other than adding a teleport homer and making him not fit in a Rhino. Honestly, the only reason to do it is because the terminator model looks so much better than the old artificer armor model.
Cato Sicarius is the Captain of the Ultramarines Second Company, and comes with quite an array of equipment and abilities that suit his station. His artificer armor grants Feel No Pain, which combines with his iron halo to make him fairly durable. He has a plasma pistol and a power sword which can inflict a single Instant Death attack, so he’s got fairly good damage output. He and his squad can even have Furious Charge once per game due to his Warlord Trait.
Sicarius brings a few buffs to the army. All friendly Ultramarines units can use his LD10 for morale and pinning tests; not quite as good as Calgar’s rules but it’ll make your squads very reliable. During deployment, you can pick one Tactical squad and give them Tank Hunter, Counter-Attack, Infiltrate, or Scout. This is pretty limited because it can only be applied to a Tactical squad, but it can be very handy. In one game, you can have a Tank Hunting lascannon to deal with enemy armor, and in the next game, an outflanking Tactical squad in a Rhino to harass enemy scoring units. When building your list, make sure to take multiple Tactical squads equipped to take advantage of each USR. Finally, his Surprise Attack rule adds 1 to your reserve rolls. Handy, though not as good as his old rule to re-roll Seize the Initiative.
Sicarius is a well-rounded character, able to do well in assault while buffing the army as a whole. He went down in points as well, so he’s an entirely reasonable choice. His main drawback is that he can’t compare to Calgar or Tigurius, both of whom bring more to the army. Still, if you like his background or want a flexible army without spending so many points on Calgar, you could do worse than Sicarius.
Chief Librarian Tigurius
Wow. Just wow. Tigurius became one of the best psykers in the game at a budget points cost. He has a similar statline to a standard Librarian, but has an extra wound. His armament is extremely standard, just a master-crafted force staff with soul blaze and a bolt pistol. Nothing impressive, but that’s not why you take him.
Tigurius is a Level 3 psyker with access to all of the main disciplines, including the much sought after Divination. When choosing powers, he can re-roll any die you want, making his choice of powers very reliable. He also can re-roll any failed psychic tests, as well as re-roll and reserve rolls (successes or failures) for his detachment.
Tigurius may be one of the best support pieces in the game, and there’s not much to say about him beyond that. To add even more utility, his Warlord Trait allows one unit within 12” to re-roll missed to hit rolls once per game. Tigurius is cheap and extremely useful in most army lists, and I wouldn’t be surprised if many players take Ultramarines Chapter Tactics just to have access to him.
Cassius is a tough but bland character. He’s a standard Chaplain except he’s T6 and has Feel No Pain. This isn’t very useful for tanking wounds from shooting, but he’s extremely hard to kill in close-combat. He also comes with Preferred Enemy (Tyranids) and a combi-flamer with hellfire rounds. Not bad but nothing exciting.