The total amount of energy available for a spacecraft to achieve final velocity is locked up in the fuel it carries aboard (we're assuming our source of energy is within the rocket, carried as fuel, not external as in scoop ships, laser-pushed sails, etc. This will always be the same, regardless of the type of fuel we use, be it fission, fusion or chemical. In short, the total available energy locked in the fuel depends on how much fuel we carry. The more fuel we carry, the more energy we get. Of course, the amount of energy we get per kilogram of fuel depends on the type of fuel and the kind of rocket motors we use, etc. But that's engineering, we'll worry about that later. Let's do the science first.

Even in a perfectly efficient rocket, not all the energy in the fuel goes into pushing the rocket. A good part of the energy is consumed pushing the unburned fuel you'll burn later. Sure, the more fuel you carry, the faster you can go, but it's a diminshing returns affair. That unburned fuel is heavy, it takes energy to move it! To figure out how fast you can go, we use the Tsiolkovsky Equation.

As it turns out, some of that total available energy locked up in the fuel eventually winds up as the kinetic energy of the empty rocket as it coasts along after the fuel is used up. Even in a perfectly engineered rocket, one that uses all the available energy without wasting any, a lot of that energy went into getting unburned fuel moving, not into getting rocket moving. There is no way we can get around this with better engineering, its a physical fact of nature. When you actually do the math, it turns out that there is a certain amount of fuel that allows you to get the most vehicle kinetic energy per kilogram of fuel that is possible. Sure, you can go a little faster by carrying a lot more fuel, but it isn't worth your while becuse your rocket payload will be mostly structural supports for the extra tankage you'll need to carry the extra fuel.

The optimum cut off point is easy to calculate, and it turns out to be almost 4 tons of fuel for every ton of rocket (3.92 to 1 to be precise). At this mass ratio, about 65% of the total energy available in the fuel goes into final kinetic energy of the empty rocket. These numbers hold no matter how sophisticated or advanced your propulsion system is.

The highest possible total available energy in a kilogram of fuel is found using the Einstein equation, E = Mc**2. As we have seen, only 65% of that goes into the rocket.

But realistically, we're not going to be able to convert our fuel mass completely to energy and capture all of that for propulsive purposes. The best we can probably do is something like fusion (we know that works, it happens in the stars and in our H bombs). But this is at best about a 1% conversion of matter to energy. Just how fast is this?

It turns out to be about 23% of the speed of light. And I'm liberal in my estimate, most other analyses play it safe and tell us fusion and fission is good for about 10%, at least for a single-stage vehicle. (See the British Interplanetary Society study of the Daedalus Probe and the Dyson Orion Project). Even with the best tech we can conceive of today, one-way travel and flyby missions to the solar neighborhood will be a matter of decades and centuries. There will be no stopping to look around and no return trips.