[daveslash]

I'm not a KSP pro, but I have tried and tried to fly into the sun and have yet to succeed. Even if I do my best to lose as much of the planet's orbital velocity as I can until I'm out of fuel, and I begin to fall towards the sun.... I still always miss and then just go into an elongated elliptical orbit. It's really hard.

[Filligree]

You'll want a bi-elliptic transfer orbit. And probably a larger rocket.

[LorenPechtel]

I would suspect that a slingshot at Jool would do it but I've never tried.