NPSfag here who worked in Natural Resources. Employee housing is typically for seasonals, though there may be long term availability depending on the park. The more remote or the bigger the park the better chance you have.
A degree is definitely required now. Most of the older workers maybe had a bachelors when they started working, but times have changed. Anything past a GS 5 or 6 requires at least a masters or an insane amount of experience. Entry jobs are GS 3 and 4
I suggest doing as much undergrad research and leadership stuff as you can, volunteering, etc. Stuff to make you stand out. Also, when crafting your resume, the conventional wisdom is to keep it short. Don't do that with federal resumes. Write out EVERYTHING that you've done. The more you out out, the better chance you have of getting past the weeding out process. After you get refered, email or call the hiring official at the park and tell them you're interested still in the position a few days after you get the email.
At first you'll probably only get seasonal jobs, then, after a few years you can build up to a term, then maybe a full time job. You will have to apply to an ASSLOAD of jobs to get one. I grabbed two seasonals this year and applied to 100.
Smaller less well known parks are great for getting experience in all aspects of the park service. Once you get a job branch out and do everything that you can. This season I taught myself GIS and created a database for the park I was working for, that shit looks great on a resume.
The important part is be flexible about where you apply. I've had to move all over the country for work. It's really difficult to stay in a geographic region if you want to work for NPS
Also AMA
