Everyone has seen countless grainy photographs of so-called flying saucers. The basic facts will debunk the idea. In outer space, there is no gravity or air. So a saucer is rather inefficient. A smarter idea would be a cube or spheroidal design.
Propulsion with chemical rockets is useless due to the incredibly poor specific impulse. Ion propulsion can achieve a much higher specific impulse. A Hall effect drive can also achieve a high specific impulse. Generally any photon based propulsion system also has a high specific impulse. Maximum power output however is still limited at present.
Specific impulse (usually abbreviated Isp) is a measure of how efficiently a reaction mass engine (a rocket using propellant or a jet engine using fuel) creates thrust. For engines whose reaction mass is only the fuel they carry, specific impulse is exactly proportional to exhaust gas velocity. A propulsion system with a higher specific impulse uses the mass of the propellant more efficiently. In the case of a rocket, this means less propellant needed for a given delta-v, so that the vehicle attached to the engine can more efficiently gain altitude and velocity. Specific impulse is inversely proportional to specific fuel consumption (SFC) by the relationship Isp = 1/(go·SFC) for SFC in kg/(N·s).
The nuclear rocket engine was tested by NASA et al on December 1, 1967. The photo above shows the engine on the left and a shield in the foreground. A nuclear thermal rocket can be categorized by the type of reactor, ranging from a relatively simple solid reactor up to the much more difficult to construct but theoretically more efficient gas core reactor. As with all thermal rocket designs, the specific impulse produced is proportional to the square root of the temperature to which the working fluid (reaction mass) is heated. To extract maximum efficiency, the temperature must be as high as possible. For a given design, the temperature that can be attained is typically determined by the materials chosen for reactor structures, the nuclear fuel, and the fuel cladding. Erosion is also a concern, especially the loss of fuel and associated releases of radioactivity.
An interesting approach to faster speeds is easy. Paint one side of the spacecraft black and one side white. By changing the orientation of the spacecraft the gravity of a star can be leveraged to reach relativistic speeds. Light impacting the white side tends to be reflected which pushes while the black side absorbs light which is a differential that can achieve a spectacular specific impulse. The advantage is that any resources on board can be used for science.
The cube shaped spacecraft, with 3 sides white and 3 sides black, can reach 99% of the speed of light quickly. It can with some simple planning reach anywhere in the galaxy desired. With some more advanced calculations it’s even possible to reach Andromeda or any other galaxy desired. The mass of the cube is driven by science not by fuel. A few stars is all that is needed to achieve relativistic velocity. Flying past stars can leverage the energy of the star itself.
Atomic batteries tend to not last very long which is an undesirable trait for deep space applications. It may be that batteries with a longer service life are possible for a longer duration project.
Solar power with adequate storage can handle many needs with smaller scale microprocessors. Processors can be idled when solar power is unavailable and activated when power is available. Every solar system visited for propulsion can also be inspected for planets and possible life. The cube spacecraft can travel by several stars over its service life.