Humm - well there are 2 sides to support.
From a corp perspective, making and selling them, then logistically - having racial coverage is a good thing. It means we can move the ship from the point of construction to the point of sale. Important from a security perspective if selling outside of any alliance we might be in.
The skills tree for Capitals (ignoring JFs & Rorquals) usually favours a general progression of: Carriers -> Dreads -> Motherships -> Titans
With each capital type there then are various specialisation skills needed: Carriers -> Fighters & Repping, Dreads -> Siege Module and Capital Guns/missiles, Motherships -> Fighters & Repping, Titans -> Doomsday
Common for them all are the Navigation skills as Vac pointed out - the higher the better. Capitals can jump between systems without using jump gates (they can't use them at all) - and the range of the jump is dependant on the skills and the ship range (Capital Jump Planner:
http://www.eve-icsc.com/jumptools/jumpplanner.php). The min range I think is about 5ly which is the base distance a ship can travel. Skills will add 25% per level.
Fittings for Capital ships are often Faction and hence expensive. By the time you are flying a capital - you should be able to T2 fit it. Those extra few skill levels will make the difference and put off the day that somebody attempts to salvage your ship.
Ideally the corp will be capable of building all races up to Motherships.
Capitals are rarely used alone (unless Vac is mining in 0.0). Mostly because to jump a Capital generally needs 2 people (excluding the POS Cyno generator).
Fleets that Capitals are in consist of 2 types of hostile action:
SiegesHere you are generally sieging a station, POS or another capital ships. Dreads are used in POS sieges as they have a special module (Siege Module) that puts them into an mode where they take very little dmg and get a boost to the dmg they do. Carriers aren't generally used diectly in POS sieges - instead they often provide support to those camping the gate and/or station.
OtherHere you'll be supporting the larger group by assigning fighters to them, being a system locus for them to jump in another ship when theirs is destroyed, remote repairs, etc
If you're confident about the numbers of hostiles and your tank - you may even be close to the action - although often you'll be somewhere safe at a POS or safespot.
Hence Carriers and MS's are generally more logistically oriented than Dreads.
I can't speak for the Directors of MADDI but I would imagine that the corp would support any Cap Ship pilot that is supporting Corp or Alliance combat ops.
Taking a Capital into action is the solely the Pilots choice based on their assessment of the operation. I would, however, encourage those flying Capitals to use their ship wisely but to support the strategic direction of first the Corp and then the Alliance.
The ship is expensive. At some point you will lose it. At some point thereafter you'll have another (if you don't have one spare already

).
Typical Costs:
Orca: 610m
Carrier: 800m
Dread: 1.3b
Rorqual: 1.5b
Jump Freighter: 1.6b
Mothership: 12b
Titan: 25-30b
With Carriers & MS's you'll also need to factor in the price of the fighters, which while they are only approx 15m each - you'll be able to use (with avg skills): 12 with a Carrier and 40 with a MS.
In terms of Pilots supporting the capital ship - the general advice for 0.0 applies.
1) Fly what you can afford to lose
2) Flying something small, fast & agile to close the gap and hold the target - is far far better than flying something big and powerful.
The reasons are simple - something big and powerful will lock the target slowly and have problems tracking anything smaller than itself.
When working with a carrier - you will be assigned fighters. Fighter are fast, powerful and the pilot they are assigned to can control them.
When I assign fighters - I prioritise who I assign them to based on the lock time, tackling setup, Corp members and then alliance members.
I won't assign them to a BS - because generally in the time it's taken them to get a lock - assigned fighters could have destroyed the target already.
Edit: A few little updates to the post and to let you know that we've setup the Corp wallet for this. As you find yourself a month or so away from buying the Capital skill books (which books are at the discretion of Beo and the other directors) - drop Beo or one of the directors a line and they will arrange things with you. The corp & it's fund is still young so the until the fund becomes more established it probably won't be able to fund the complete price of the skill.