Preface: This is half a guide for new players based on my experience in the game, half a discussion thread to discuss what others think.
First Tier:
SS - In MFN, player talent is far more important on defense than on offense, the secondary is the most important group on defense, and the Strong Safety is the most important of all of the secondary.
Second Tier:
DEs - Currently, the DLine is overpowering the OLine. Having a DE with high speed and acceleration will generate pressure on the QB and force hurried passes. Having two of them will give your opponents nightmares. Additionally, D-Line has about 40% longer careers than DBs which should be taken in to consideration.
CBs and FS - As mentioned before, secondary is primary in MFN. CBs and FSs aren't quite as all over the place as the SSs, but still critical to a team's success.
WRs - The top offensive position of my list comes after four defensive positions, which may be surprising. There's nothing more frustrating that watching a dominant WR come down with the ball over three of your DBs and roast them for a 70 yard touchdown. An elite WR has the best chance of bailing your team out in a last minute comeback drive.
Third Tier:
QB - Not quite as important as in the NFL. You can have success with a mediocre QB and long as he's got good targets. It certainly helps having an accurate QB though.
RB - I haven't figured it out yet, but some teams have great success with running the ball. I like a good running back because they can help secure the win by busting through for first downs while I'm trying to run the clock or being more than serviceable WR4s or WR5s in a 4-5 wide set.
LBs and DTs - Have to round out the Defense with the rest of the box here. DTs and LBs aren't essential to a team's success, but they can be a tremendous boost if they're talented.
P - That's right. The punter. I'm not sorry. I've seen Punters change so many games. Between getting a clutch pin within the 5 yard line or booming it 80 yards. A punter can save your team when your offense is stalling. I'm sure Gustoon thinks they should have been top tier though...
Fourth Tier:
OLine - As the results of the new build of OLines start rolling in, it seems like no one's quite sure of how to stop fast d-linemen right now. Some say that the boost in o-line speed hasn't helped.
TE - Sometimes they come up with a catch, but owners of Elite TEs are getting frustrated with their lack of targets.
K - Hey, they're kickers. They have one job, and always seem to blow it.
Fifth Tier:
FBs - I have never seen a game decided by the play of a FB. They have minimal impact on the game and shouldn't be too fussed over. Recently, I've been using the FB position to develop younger RBs.