J9 suited is certainly strong enough to raise from the button. Even though the hand plays very well multiway, I don't like giving value to the blinds by limping unless my hand is so weak that I'm not comfortable putting in a lot of money. For example, I would always iso raise the strong suited hands like this and I would typically limp 22 or J6s or A7o. There are certain hands that are super strong in multiway that you could decide to just iso to a very small amount like 2.5bb, A4s or 33 would be a solid hand for that, but it does open you up to being exploited by good players who know you're raising to different sizes with different ranges.
I think that the flop bet could be sized even smaller. It's a fairly dry board and you're very likely to be beaten if someone calls you 4 way, so your bet is more for protection than value. 70-75 cents IMO.
Turn spot is interesting. Betting certainly has merit as your hand is mostly good, but th eproblem here is that he just is going to fold nearly every worse hand. He could also easily have a better 9 or TT/QQ etc, so again, your turn bet will primarily function as protection to fold out his equity with 8x/2x or to get value from JT/76/T7. There is substantial value to this, however if you look at what happens when you check, you may find that the outcomes are quite good for you.
1) He's unlikely to value bet you with Q9 or TT, so you safely avoid paying those hands off.
2) If he bets the river, his range will primarily be busted straight draws. QT/JT/J7/T7/T6/76/65/75 all are plausible for his range. Many of these hands fold the turn, but would be perfectly willing to pot it into you when they miss. You can, of course, easily call his river bet on every river that isn't a 7 or T. If he turned two pair or slow-played a set on the flop, that's unfortunate, but you would be giving that hand value regardless of the chosen line. And the possibilities for two pair plus are remote compared with the busted hands.
So ultimately the decision to bet the turn depends on the likelihood it is that he will bluff his busted gutters and oesds. You will find in theory study that this is very often the deciding factor for whether to bet for protection in position in NLH.
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