Earlier quoted context omitted.
Honestly I would second the idea of just joining a company as an FTE (full time employee). Find a place you really like, interview them at least as much as they interview you, and probably say "no" to 5-10 companies before signing on with one of them. Or maybe just join your favorite client full-time if there's one that would work. Give it a shot for a year, you might like it. (source: have freelanced/founded, never…
FTE stands for ‘full time equivalent’ http://smallbusiness.chron.com/calculate-fte-742.html
It's frequently used to mean “Full Time Employee” (distinct from both a part timer and a contractor), probably originally by people who have overheard the HR speak and misunderstood what it is referring to, but the use seems to be established on its own at this point.