"There are 3 ways to play pocket jacks and they are all wrong."
I think preflop play is determined by a few factors.
Fold: If Villain is value heavy and reluctant to be bluffing.
Call: If Villain has sufficient bluffs and is capable of bluffing the rest of his stack postflop. If opponent is Aggressive postflop this option is great.
All-in: If Villain has sufficient bluffs and will not bluff post flop. Another reason to shove here is if Villain is a bit tilted and willing to get in here very light. If Villain will stack off with AJ+, 99, or even weaker.
In this particular spot I see folding and calling as the best options most of the time. For most people I think this is going to be a fold especially with that 3x sizing which is usually an indicator of KK+ish. Some more adventurous regs like to punish me a lot for being too loose so I find myself calling here a lot. If no overcards come on the flop I'm a lot more happy getting it in. If an ace comes on the flop I'm probably gonna fold.