As a business, dont get your hopes up on getting a golf course, they do that stuff in house. and chances are if you go work for a golf course, you'll be just anorther laborer, but you gotta start somewhere
in regards to fields....I would try to contact the local little leauge and public/private schools who have soccer/football fields and try to get the landscape maintenance contract wich includes the fields.
I woudl reccomend being an employee with a company who has a few fields, or work a for golf course and cut your teeth....Jumping right in to maintaining a field on your own can be a daunting task....
school education is not everything, hands on education, IE "learning by doing" can be more important....
Keep us informed at your progress