To reach 10% of light-speed, the ship would have to burn 37% of its mass; for 20% c, 61% of the mass. If you then slow back to zero, you will burn 61% and 85% of the mass respectively. 15% of light-speed would be a reasonable compromise. At 100% efficiency, accelerating to 15% of light-speed and then decelerating to rest, the ship would arrive with 25% of its starting mass, having used 75% as fuel and reaction mass. (Errors introduced by ignoring relativity are minor compared to those caused by assuming complete efficiency. Time dilation effects are only about 1%.) It takes less than two months at one gravity to reach 15% of light-speed. Even at a fraction of a g, the majority of the trip could be spent coasting.
(The rocket exhaust is powerful alpha radiation. This is an ideal vehicle for leaving your enemies behind, but be careful where you point the thing if you hope for a welcome upon your return.)
A ship traveling the 18.2 light-years to Sigma Draconis at 0.15 c would take 122 years, one way. It has to refuel (hope for a planet with a water ocean to supply lithium and hydrogen!) before returning. The round trip could barely be made in 250 years; with study time, more would be probable.
Most of the ship is fuel, a giant lithium-hydride cigar—white when pure, but who knows what impurities will creep in (or be found useful)? The long axis points in the direction of travel, to minimize cross-section and put as much mass as possible between the crew and anything they collide with. (At 0.15 c, cosmic gases become low-energy cosmic rays: grains of dust make large craters where they hit.)
Well ahead of the cigar is a repairable “umbrella” shield—very little mass, but enough to vaporize cosmic dust, spreading it out so it’ll cause less damage to the main body of the ship. The living quarters are inside the “cigar,” protected from the hazards of travel. Spiral tunnels wind forward and aft to the end caps; since radiation travels in straight lines, a spiral tunnel blocks it effectively.
A fusion rocket is behind the cigar, built of magnetic fields controlled and confined by superconducting magnets. There are many magnetic mirrors in series, so a particle leaking through one mirror finds itself confined in the next chamber. The fields move the ionized gases along in a manner similar to peristalsis with regions of high and low magnetic field sweeping aft. Ionized particles are held in the regions of low magnetic field by the stronger fields before and behind, compressed to greater and greater densities until they fuse. At this point the magnetic fields to the rear open up into a rocket nozzle of forces.
The rear-end cap slowly chews its way up the length of the ship, feeding fuel into the engine. The amount of lithium hydride before and behind the living quarters is chosen so the engine uses most of the rear fuel accelerating: then, as the ship nears its destination, the end caps are released and the ship reversed so the forward section (now needed more for fuel than shielding) docks into the engine. The umbrella shield is discarded as excess mass, and will be rebuilt during refueling.
Deceleration poses an interesting problem, since one can hardly put an umbrella shield behind the main engine. But the hot breath of an engine like this should sizzle nearly everything within a light-day of the nozzle into ionic vapors—and the engine’s magnetic fields protect the ship from ions. An arriving ship appears as an enormous dim comet, with tail pointing along its path rather than away from the sun—and like comets of old, it can be an omen of change.