How should I approach Jool to make best use of my fuel?

Suppose I want to land a kerbal on one of Jool's moons, say Vall, for example. How should I approach Jool to make best use of my fuel, without using aerobraking? What kind of orbit should I shoot for? Low or high, circular or elliptical? Or should I try a direct encounter with the moon instead?

I think that the most efficient way is aerobraking (thus, the orbit altitude is as close as possible), but my rocket doesn't have the necessary aerodynamics nor heat shields for that. Not sure what the next best thing is.

I have been to Jool and some of its moons a few times, some successful, others not so much, each time approaching them differently, haphazardly, never knowing what the best approach is.

I have researched this a lot, but I only find discussions about the best parking orbit at the origin, and the videos about traveling to Jool usually speed up at the arrival, and I can't quite figure out what's the best approach.

Solution 1:

Jool is great for gravity assist maneuvers due to the very massive moons. The general rule of Gravity Assists is that you pass behind a body to gain speed and in front of a body to lose speed.

So as soon as you enter Jool's sphere of influence, plan a burn to make your trajectory pass very closely in front of Tylo. This should usually just cost you a few m/s² of delta-v and get you into an eccentric yet stable orbit around Jool.

As soon as you have an orbit around Jool, you can plan further encounters with the moons to adjust your orbit further. It won't allow you to get into the orbit of a moon, but it can get you quite close.