Background Material Evaluation.
The background for the Ultramarines is what can be expected for this most glorious of legions. Not satisfied with simply conquering and destroying, the Ultramarines were a legion very keen on rebuilding an empire once intransigent leaders and popuplaces were subdued. In addition to this, it is noted in numerous locations within Tempest and other Horus Heresy sources that the Ultramarines legion is the largest of all the legions, larger than even the Word Bearers.
There are many little Easter Eggs and gems contained within Tempest about this legion. This includes for instance the existence of a lot of "Chapters" that would later be formed in to 40,000 chapters from the gene-seed of Roboute Guilliman such as the "Aurorans".
More than this, their domains cover an entire sector, popularly referred to as the 500 world. For this reason, and their relative strength, Horus calculated correctly that a hammer blow had to be landed against them to take them out of the coming civil war. The Word Bearers would be the ones to do this at Calth, and the World Eaters would later join them in the Shadow Crusade.
Legion Rules Review.
The Ultramarines special rules reflect that they will eventually become the prime example of codex space marines in 10,000 years time. They result in the Ultramarines being a curious hybrid of 30k and 40k space marines, but neither wholly. They lack the specialisations of other legions, but make up for it by being able to be good at most things.
Their first rule is Interlocking Tactics. This means that to wound rolls & armour penetration rolls of "1" can be re-rolled if a target has already been hit, and other units charging in must re-roll their charge distances if they don't make it in to close combat. This begs the Ultramarine player to take small units that are going to usually hit their target (even if they don't necessarily harm or can harm it). For example, a legion reconnaissance squad would be perfect to set this up with. Take a minimum number, and have them hit the target. Then go all out with a fully armed and upgraded unit (maximum tactical squad with Fury of the Legion perhaps, or how about lots of volkite shots from a support squad, or even lascannons from a heavy support squad against a tank that was merely hit by a sniper rifle?!).
Certainty and Resolve means that the Ultramarines are taking fear and regrouping rolls on the maximum Ld of 10. This can be really useful should they be up against Night Lords for instance.
Given how amazing these two rules can be, they have a counter balance in the form of a Rigid Chain of Command. Should all HQ units be slain, the enemy gains +1 victory points. This is kind of an analogue of what can happen to the Alpha Legion in some ways. But it is actually worse. If the warlord is slain, then all units without an independent character must take a pinning test. This can be crippling (recall that the Ld of space marines isn't always 10! -- several units will fail here and this can completely alter the course of a battle). Naturally, one way around this is to take multiple HQs. Ensuring some Centurion is knocking around is therefore a good idea for the Ultramarines in addition to their primary HQ selection.
Selecting between all the forms of power weapons, Guilliman came up with the Legatine Axe. This is a terrific AP2 axe that goes at initiative and a hit of a "6" automagically wounds! This is well worthwhile for an independent character and worth the points cost. Do it.
The Mantle of Ultramar is for praetors only and gives an artificer save as well as feel no pain. This is in addition to blindness immunity (should you be facing some Iron Hands' Gorgon Terminators). Its cost is moderate and probably worth it just for the feel no pain bonus (just).
Rite of War.
The Logos Lectora is an interesting rite of war that merits thought as to whether a player should take it or not. On the one hand, it can certainly provide of quantum of versatility and a special rule when it might matter most. But the downsides are steep including no deep striking and infiltrating. Yet the ability to reroll some runs, make snap shots on a higher BS and gain counter-attack could be huge. It just depends if the player is willing to take the hit in terms of army building capacity which can be significant (and might mean a legion player using the Alpha Legion or Raven Guard could readily gain a great edge over them).
The special rules associated with the Ultramarines calls for at least some of the army to be composed of small units. And several of them. This "multiple small unit" approach will be familiar to many Warhammer 40,000 list builders and players across numerous editions. But here in 30k, its something of an anomaly where going big is usually the way forward since it provides more things for cheaper points. Therefore some balance has to be built in. A few small recon squads for activating interlocking tactic's bonus to hit with ranged weapons seems sensible. Add to this some maximum squads to take out tanks highlighted by the recon squads, or volkite spamming units to take care of infantry and you get the idea. A tar-pitting unit like terminators may also sound good for taking on large enemy squads to gain a bonus for others to pile in, but I don't think this is the way to go here -- focus on the shooting and take out enemy units sequentially.
The main weakness here is some inflexibility. Against hordes, the Ultramarines are not going to do so well in all likelihood. And spare points to spend on nice upgrades might be limited since there is going to be multiple small units that chew up points (as opposed to expanding already existent units). This needs a careful approach to balancing an army.
All this said, the Ultramarines are a force to be reckoned with. Just because they're the "vanilla" chapter in Warhammer 40,000, they can still really shine in 30k. Focus on taking out enemy units with shooting one unit at a time by highlighting said unit with something like a recon squad and rinse and repeat. Combine this with some (rather good!) melee units that are specific to the legion and its a good basis for a force. Add in some tanks (or ally with Solar Auxilia, or Iron Hands) and you're good to go. Just beware of other legions being able to be more specialised than you, and then play to your strengths against them.
And finally, laugh at the Night Lords legion and their fear tactics (should you get the opportunity) when you tell them about Certainty and Resolve!