If you host the co-op lobby and manage to complete all six missions in order, in one sitting, you'll get an exclusive "hidden" vehicle. The Enus Armored Paragon car is spawned at the docks if you are eligible, and cannot be acquired in any other way.
There is another bonus payout of GTA$ 500,000 if you manage to play through the six missions in order the first time you play them. If you play the missions but don't finish them in order, you won't have another chance to try for this bonus, ever. This adds on top of the other first-time completion bonuses, and the bonus GTA$ 50,000 gained from every mission completed without a death.
Note that co-op missions cannot be played solo. There is also no way to ensure that you are the host of the given session — it's a gamble!
In addition, to be able to progress within the co-op missions, the host must elect to do so. So unless you are hosting yourself, or get lucky with a competent host, you might be stuck repeating the same mission. Currently, there is no easy workaround for this.
You can keep retrying when joining Casino Missions to see if you get lucky by being the host. Keep in mind that to get the Host bonuses, you need to play through all six missions as host. If you've been playing through them but only Host the last one, for example, you don't get the Enus Armored Paragon.
The other kind of missions are Casino Work Missions, accessible by calling Agatha Baker. These are less lucrative than the co-op missions and lack the overarching storyline, but can be completed quicker and alone.
Services
Once you become a member of the Diamond by purchasing a penthouse, you can call Agatha Baker for one of three things. These services are entirely free of charge. These are not available if you have a wanted level.
Car Service
You can call Ms. Baker to request a vehicle to be spawned. The options are limited, with the Cognoscenti Cabrio, the Windsor, the Fugitive, the Super Diamond, the Dubsta, and the Feltzer — the fastest among the choices — being available. You don't need to own any of these vehicles to be able to order one.
The spawned car cannot be placed into a garage or insured and the game does not consider them personal or Pegasus vehicles giving them a new marker. The cars aren't stock, but carry certain upgrades such as bulletproof tires and performance upgrades.
Note that the cars are set to public access, so any other player can enter and steal the car if you're not careful. The vehicle will spawn right next to your character when called. If you enter a building interior the ordered car will automatically despawn. There is a 2-minute cooldown for using this service starting after the vehicle is spawned.
Limousine Service
The limo service works in a very similar manner as the taxi service, but as mentioned previously, is free for penthouse owners. When called, the limo will spawn right beside the player and can be either white or black. When you sit in, the limo will automatically drive towards the Diamond, but you can also set a waypoint and it will drive you there.
The limo driver will not be intimidated by attacks or weapon use and will only exit the limo if it flips over. This feature makes the limo a perfect getaway vehicle if you need to escape from cops, enemies or other players. You can kill the driver and take the car, but it cannot be stored or tracked, and doing so will yield a wanted level.
You can give the driver various instructions, such as to speed up, slow down, or to stop entirely.
An additional feature of the Limo service is that when called from your penthouse's landline, or ordered from the Diamond Casino's front desk, it can be used as a free fast travel feature instantly transporting you to one of the locations marked on the map below (made by @borqer):
