We are already past chemical rockets. Ion Thrusters are a thing and can get you going 100 times the propellant velocity of a chemical rocket. I presume the ship would have a nuclear reactor rigged and sized to work for the journey with solar panels to power most of the propulsion. The ship will first thrust deeper into the solar system to get more solar power and set up gravity assists with Venus to reach Jupiter and then a grand alignment with multiple gravity assists on the final way out of the system to get itself going the right direction. As they leave the system and solar power falls off they'll have to throttle down. Maybe they'll have electro-static collectors to collect stray hydrogen on the way that they can feed into the Ion engines using whatever spare nuclear power they have each day. Then reverse the process upon arrival.