I'm pretty amateur at all this too but first thought is that if the fields are that boggy then all a tractor is going to do is make horrid ruts.
If you have a good depth of soil then drainage is the first priority to my mindset BUT local conditions vary and the simplest answer is local knowledge.
I'd suggest asking the nearest farmer for advice and help..if it's anything like my area he'll probably know your field's history anyway.
The other way to find help is to go see the nearest agricultural engineer on the grounds that he'll know most of the farmers and who is frindly or a miserable B to approach.. and may well do some contract work himself if needed. Final option is local pub - I go down at least every 2 weeks; less for the beer (or so i tell the wife) and more to keep in touch with the local agri workers, the scrap merchant, the hardware shop owner and similar folk who drink there. Between them they have most answers and enjoy taking the mickey out of my puny efforts...