When I saw who Wichita listed as folks interested in the raid group I was happy to see who there. Then I saw what people want to play and I cried. When ret pallies are more popular than locks or hunters you wonder how long it would take to kill a boss. Healing is also not real popular either. I don't mind full time healing but I think one resto druid would be enough. Anyway I thought I would list what in my mind would be the perfect 15 for a 10 man raid guild.
1 Prot Warrior
1 Prot Paladin
1 Death Knight
1 Feral Druid
1 Holy Paladin
1 Resto/Balance Druid (depending on what is needed)
1 Resto/Elemental Shaman (depending on what is needed)
1 Holy/Shadow Priest (depending on what is needed)
1 Enhancement Shaman
1 Ret Paladin
1 Priest of any sort
To me that covers everything, no fury warrior, but the group buffs brought by the enhance shaman/ret paladin put them at the top for me. If there was an encounter where you would want a balance druid and a tree druid you wouldn't have that, but I'm guessing there aren't many of those. You should be able to make a strong melee or caster dps group out of this. There are also no more than 3 of any class.
The group that went any given night would depend on people's availability and the encounters being done, since this is ideal people will be there when needed. I would think you would want one prot warrior/pally and one feral druid/Death Knight to cover tanking. Five dps, whatever you can get that night that would be best for what's coming up. For healing two heal specced healers and one moonkin/elemental shaman/shadow priest if any extra healing is needed. Since healing and dps gear will basically be the same the off healer won't have to switch much making it way easier to gear to heal and dps than it would be for a ret paladin or enhance shaman.
I don't think you "need" all this to have successful raid. I don't think you have to take the perfect group and sub out people for fights. If your pool of players lacks depth of classes/specs you're making life much harder on yourself. I'd personally like to just prepare to have my druid for resto/balance heal or dps as needed, but we have 4 druids. We don't need more than one rogue, we wouldn't need more than one hunter either. So I might re roll something, who knows? That's all.