There is a most important stat, but its not probably the answer any new player is looking for. That would be Stamina. In order to play well at all you need to have it high enough to compete with those around playing against you. These levels are different depending on SMJHL or SHL, or what line you play on and how much ice time you get. But that is the foundation for playing well. Fortunately the stat is so important that they raises the floor to 11 so you cant truly screw yourself over with low stamina.

As far as the fun things for each player type, there isn't a magic stat like shooting or defense like in STHS. You need to be well rounded to play any position. It may be tempting to dump all your points into something like Shooting Accuracy, or Passing, in order to instantly shoot up to being the best there is at your role, but it doesn't quite work like that. Especially with the TPE scale. There's no way to game the system purely with skills (that we know of). But there are a few key stats that everyone should be aware of.

Offensively, Getting Open is a surprisingly useful stat. It has a high correlation with how well forwards and especially shooters perform. This is because it directly increases shots on goal, AND increases the quality of those shots. More shots = (hopefully) more goals and more wins. Other honorary mentions are Puckhandling and Offensive Read. These are always a good choice and will help keep your game running smoothly. The best defense is a good offense. But if you are defenseman, know that shooting range is much more important for you, and worth investing deep into unlike forwards who don't necessarily need to max it out even at the low cap of 12.

Defensively, Checking and Defensive Read are the name of the game. These are important for everyone if you don't want the other team running over you, and your coach will love you for investing in these. Checking and Defensive REad apply to every situation defensively so they will always be relevant if your team doesn't have the puck. Other defensive stats are more situational based on your role, but if you are a defenseman then of course Shot Blocking and Hitting are priorities. Centers will need faceoff skill.

For physical stats, Hamilton has pioneered the importance of Strength and Balance in their physical game, and if you want to keep up you need those too. Pairs well with points in hitting but not necessary. The other stats are never a bad place to put points though. Unless its fighting. But if you want to put points into fighting you probably already made up your mind about it.

Mentally, there's not much of importance. We're all too dimbi for the mental aspects of hockey - that's why we play by writing PTs. You only have two options in here and one of them is only used by that fighting type of guy I described above. The other is bravery and its not terribly important. Most put a few points in and call it a day.

Goalies: I have no idea. I'm not a goalie and you guys are whole different ball game. Good luck.

To recap: Everyone needs Checking, Defensive Read, Strength, and Balance. Forwards need Getting Open, Puck Handling, and Offensive Read - though defensemen should still take note. Defensemen specifically need Shot Blocking and Hitting. Goalies need Jesus.