In terms of federal park/forest service LE positions, like others have said, they are very hard to get especially the 1811 spots. The BLM academy was run out of the same FLETC I went to and I became friends with several of them. Most, if not all of the BLM recruits at that time were Native American and many were prior Tribal Police Officers and or state/local park rangers before being hired by BLM.
I wouldn't bother with a self sponsored academy if you are looking into federal LE. You will have to go through FLETC regardless of whether you are an entry level applicant right off the street or if you are a seasoned LE veteran.
Another good option if you just like working outdoors is the Border Patrol. The work is almost all outdoors and there is a good deal of interaction with BLM, state/local park rangers and other LE organizations. It would be a good spot to get your career started and to start networking. Plus it will give you federal time towards your retirement and other federal benefits that would transfer over should you ever choose to move on to BLM.