Well done on your degree. They'll be someone along later that will help you out I'm sure. One thing I do know is volunteering is a really good way of showing that you want 'in' and if you're passionate enough about wildlife and conservation, you'll stand out.
When I got my field teaching job, I took along a portfolio which showed that wildlife wasn't only the job I wanted but the fact that it also entered other areas of my life- eg hobbies and spare time (ps I don't have any now because of my job and hobbies

).
I suppose the rest will depend on what you are prepared to do. There's loads of different conservation bodies that have jobs for volunteers,so get on some lists and get inside the door. You may find that then you'll find what you do find the job that you want and also what you don't!
Good luck and I hope your career is a great one.