What class is the most effective/cost efficient for casting rituals in D&D 4e?
Wizards gain rituals more easily than any other class; they start with three rituals for free, and learn two more for free at 5th, 11th, 15th, 21st, and 25th level.
Bards only gain two rituals for free at first level, but they can cast one bardic ritual at no cost every day. At higher levels, they can cast two or three free bardic rituals per day. So they pay more up front than wizards, but they can cast for free, which wizards cannot do.
Other classes with free ritual casting are all more limited in one way or the other (up front costs or casting costs) than wizards or bards. For completeness:
Artificers gain Brew Potion, Disenchant Magic Item, Enchant Magic Item, and Make Whole for free at first level. They can use Disenchant Magic Item for free as often as they like.
Psions gain two rituals at level 1; one must be either Sending or Tenser's Floating Disk. Once per day, they can cast whichever of those two they chose. This is less choice than the bard has, and they can never cast their ritual more than once per day.
Invokers are exactly like psions as far as rituals go, except that their second free ritual is Hand of Fate. They can cast Hand of Fate once per day, and never more than once per day. Druids are like invokers, but have Animal Messenger instead of Hand of Fate.
There are also various feats which reduce costs of ritual casting, but since any class can take them, I don't think they represent a difference between classes. I will note that there are a few feats which allow PCs to make magic items with levels higher than themselves, but again, these are not class specific. They are often background specific, though.
For lower level rituals, I'd say any class trained in Arcana with the Experienced Arcana (daily Arcana utility 6) or trained in Bluff with Improvised Arcana (daily Bluff utility 10) Skill Power Feats from PHB3. That reduces the cost by half for rituals that are less than half your level (except for Brew Potion and Enchant Magic Item, of course).
The "best" ritual caster class is one that satisfies the following parameters:
There are 314 Ritual-like practices, martial practices, or alchemical recipies:
No-check skill training can be accomplished through backgrounds or multi-classes. The important check-based skills are Arcana (Int), Heal(Wis), Nature (Wis), and Religion(Int) (as expected.)
Assuming that only one player is interested in this, we need a way of getting maximal checks and the most free casts with the least investment.
The best feats to ignore ritual costs are the Vistani feats. Choose whichever ones the group would like you to cast every day. As the classes are quite broad and grant synthetic ritual casting as well, they are a fantastic way of getting cheap rituals. I strongly urge the aquisition of the vistani Pathfinder ritual, as that provides the party with 1 free teleport a day, as well as the fantastic Traveller's camouflage.
The items from Dragon 387 are strongly recommended for the ritualist, as they all enhance certain rituals quite neatly, as well as serving as focuses for them. The Ritualist's Lectern is also an essential piece of kit for this purpose.
Curiously, the best ritualist class is not one of the ones that gets ritual casting for free: Shaman.
The best class for ritual casting is a Deva Stalker or Watcher Shaman, with the Bardic Training, Vistani Heritage, and Vistani Pathfinder feats. Bardic training grants ritual casting and a free bard ritual a day (quite nice) and vistani pathfinder grants a free travel or exploration a day. The vistani feats are optional, but present significant utility.
The reason for Shaman is the following power:
The idea is that you use it before making the check at the start of the ritual (as there's nothing that suggests when the check happens during the ritual, and it makes sense that it happens at the start, a "do you know exactly what to do and how to do it?" concept.
The Deva can then use memories of a thousand lifetimes to add another 1d6 on top of that. There are additional feats one can drop, of course, but over-specialization is bad.
As a deva watcher shaman, level 1, with the bardic training feat. Int 18 (base 16), Wis 18 (base 16), Cha 13.
Training in all 4 of the ritual skills. (one through multi-class) and the High Imaskar background (if allowed) or a +2 arcana background if not, presents:
5 (Trained) + 4 (Stat) + 4 (Speak with Spirits) + 1d6 Memory of a thousand lifetimes + 1d20 average check result of = 27 at level 1 for any of the 4 ritual skills, free reroll on arcana (must take second, so only use it if the first roll presents an active problem) and +2 on religion from racial.
The Ancestral Incarnate PP has a fantastic level 16 power to enhance ritual casting, and is a solid PP on its own. (The level 12 utility is worthless but very flavourful.)
There are a number of handy utility powers as well:
For Wizards, or if you chose to go with the wizard MC (easier to satisfy without the charisma requirement, and the Vistani Jongelur feat satisfies the bard rituals), the tome adept has a daily +10 to a ritual, as well as other buffs.