Igor.
If this is a solved problem, then my fears are unfounded. Let me know.
In that context, the remote possibility that a rocket might accidentally fail in a way that somehow managed to crack open its little reactor, spilling some radioactive material in a way that somehow harms anything whatsoever, would seem quite trivial. I'd be more worried about airliners crashing into me on the freeway if I were you.
In other words, I'll bet you five bucks that nothing radioactive will drop onto your house the next time they launch a satellite with a nuclear reactor onboard.
... Which are potentially even safer, because the fuel is not terribly radioactive until it has actually been in the reactor. Ship it up in parts, assemble when safely in orbit.
And I remember reading that we are a little short on the right fuel for those right now, since it has not been manufactured in years.
Ha ha, I told a funny!
A working fusion device of almost any kind would open up the solar system, without the dangers of lofting fission reactors. (Also, they get better energy density, and while fission would probably cut the mustard, in space you'll take every bit of energy density you can.)
Igor.
(Besides, it might be possible to launch a running Bussard reactor, jumpstarted on the ground. Given how it works, 8 or 10G vs the 1G it already has to work in may not be a significant difference. It almost certainly would be possible to launch a running focus fusion device, though I'm a lot more skeptical about that one. Well, I'm skeptical about the whole field, but some are more plausible than others.)
The nice thing about these is that there's only a few kg of radioactive material, and an accident high enough to generate fallout will also burn up both the fuel and the shielding.
Instead they are actually designed NOT to burn up, but rather fall to the ground in one piece.
The orbital infrastructure could consist of mirrors, which would be relatively lightweight.
Let's say 3000 lb of weight for 1 lb of constant acceleration - time to break at other end of trip. Add in a pay load we are talking ~1/5000g which still get's you 2km/s after 12 days. This would take ~300 days to get to mars. But, you could still accelerate on the trip. You would need to adjust for the loss of sunlight as you get further from the sun, but I think something like 120 day's might be possible with solar power.
Granted all of this is orbiting the sun, and you can get a little boost from a close approach to the moon etc.