order to leave the surface of Earth and go someplace else in the
system, you need 63 megajoules per kilogram of final weight to exit the
gravity well. In order to leave our sun behind from a distance of 1 AU,
you need to have 890 megajoules per kilogram of final weight. This is
cumulative, so to leave Earth and then exit the system with 100%
efficiency requires almost a gigajoule of energy per kilogram of ship.
If you began at a radius of 1 million kilometers from the center of the sun - which is to say 300,000 kilometers from the surface - then you'd need 133 gigajoules per kilogram of ship. In general, the energy to leave is E=m1m2G/R, by conservation of energy. To go from R1 to R2 from a mass, the change of energy ΔE=m1m2G(1/R2-1/R1).
Also by conservation of energy, a ship can actually carry on board no more than its mass in energy. An unmoving ship has just under 90 petajoules per kilogram by the modern definition of matter; it is merely a question of how much of this energy may be accessed how quickly. Generally, the portion of the ship with accessible energy is known as fuel, and the energy of the fuel refers to how much of it is released - up to the full ~90 PJ. This efficiency is achieved theoretically with matter/antimatter reactions and other "pure" mass/energy conversions. More common are fission/fusion reactions; using such, the highest available rate of return is the annihilation of up to 0.89% of the mass of the fuel, generating ~800 terajoules per kilogram by fusing protium or deuterium directly to iron 56; even fusing "only" to helium gives ~600 terajoules per kilogram.
Of course, hydrogen is inconveniently light, but metallic hydrogen runs to 1.3 tons per cubic meter; we can hazard to guess metallic deuterium would be about 2.6 T/m3, which would give a maximum energy per unit volume of fuel of just under 2.1 petajoules per liter of stored fuel. Metallic tritium would provide just a bit under 3 PJ/L, but its instability and rarity in the natural world make it a far less practical fuel, and thus not likely.
Deuterium/antideuterium slush, if half crystalline and half liquid by volume, would provide 14.2 PJ/L at a total density of 0.158 kg/m3. Simple deuterium slush fused would give 100-115 TJ/L.