So to answer your questions fairly specifically...

MGP is the "special" currency they use at(and only at) the Manderville Golden Saucer. At/around level 15 a quest in Ul'Dah will open up access to the saucer. At the same point, a quest in Limsa will unlock your "Challenge Log". Do both those quests. At the saucer you'll have sub-quests to unlock chocobo racing, triple triad, and verminion - do all these too. At the saucer there are small minigames you can play to earn endless MGP in small doses, there are GATES(saucer version of fates) that can earn you thousands per pop(one spawns every 30 mins - 15 and 45 past the hour), there are your bigger minigames(triad, racing, verminion), and there are the lottos. Mini-Cactpot is up to 3 daily scratch off tickets worth potentially 10k each, Jumbo Cactpot is a weekly drawing with a tiny chance to win over a million MGP in one go(and smaller consolation prizes). Try all the games once or twice to get a feel for them. The challenge log will have bonus objectives you can meet for bonus MGP that can be repeated once per week each(along with bonuses for a lot of other parts of the game - VERY worth it). Then decide how much effort you want to put in. If you decide to basically "move in" to the saucer, you can grind out 1 mil in a few weeks of constant gates and games(or you can get lucky and win this weekends jumbo and get there in 3 mins work). Most people get there in 3 or 4 months of regular but casual trips to the saucer. If you're taking the "slow" approach: do as many challenge logs as you can, do your mini cactpots as often as you can, enter all tournaments(even if you dont really play, the participation prizes are worth the 30 seconds registering takes), do the gates that you enjoy, and youll have the money built up soon enough.

And dont worry about your company, it wont matter on this topic.