Some issues which quickly came into mind from reading the thread title:
1. How do you lift a nuclear reactor big enough to support life into space?
2. How do you reduce the risks on life with using a nuclear reactor onboard?
For the first question, it does not really have to weigh all that much. Consider, as an example, a simple short-halflife "reactor" (there is no real chain reaction going on, it's just that the material naturally has a short halflife, called a radio isotope thermoelectric generator, somtimes called an "Atomic Battery").
They included one using plutoniumin-238 the pluto probe, around 10Kg, and it produces 500W+ (at 10% efficiency, so 5kW of heat..) for some decades (87 year halflife, so 50% of the efficiency after 87 years), without moving parts (using thermoelectric elements).
If the weight budget was somewhat higher, say, 200Kg, you could perhaps build a simple steam turbine, which would give 30% or so efficiency.
As for the danger, how exactly would a nuclear reactor in space, even one with a chain reaction, be dangerous? First, there is no air to spread particulate matter (which is the normal risk with reactors on earth, you breath in the particles, which can cause lung cancer, or eat them, which can cause replacement of non-radioactive isotopes with radioactive onces in the body, which over time can cause cancer. Note that we always have a lot of radioactive carbon in us, though. :-)).
Let´s take the nuclear battery version, as an example. The plutonium releases alpha particles, which are stopped by 10cm of air, or a thin paper, not to mention the radiation screening, or the encapsulation of the individual plutonium particles in the reactor. Alpha emitting materials are chosen because the radiation is so easy to stop, which converts it to heat. You will also keep your power station outside the main habitation areas, presumably.
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If you forget about current laws regarding nuclear reactors and space (it's forbidden) and about some other stuff, you could most likely get up to 50% to 70% lightspeed (just a guess, not calculated right now, so all numbers are most likely to be lower/higher as in: it takes longer). Still fast, but since the next star is already more than 4 Ly away it would take ~8y to get there, acceleration and deceleration included. You'll have to use low acc and dec since you don't want to kill your travelers.
Oh, and don't forget the fuel to return. And the materials you need to build stuff there. And food. And...
Actually, even using the most efficient possible theoretical fission powered system (10M degrees exhaust, using the spent fuel as an ion drive, at 100% efficiency) will not get you more than 5% or so of light speed, give that 99.9% of the spacecraft is made up of fissionable materials. And you will not be able to stop on the other side.
You need fusion to get anywhere at all, and even that will only get you a 10x improvement (20% of light speed, at 99.9% fuel to payload ratio, and you can stop. However, the fuel is rather easy to get in this case, at least if we master hydrogen-hydrogen fusion and use oxygen as the main reaction mass. Simply mate a large chunk of ice (a few million tons, say) with a power plant and engines, you can then have a few thousand tons of payload, and water and oxygen is no issue, at least. :-)).
You would probably accelerate in the sub-0.01g range, though, over a rather long time. So, let's make it a big asteroid which we rotate around the axis of motion (this also helps to balance any eventual small imbalances in the drive) with the actual living environment attached to it on a long arm, swinging around to produce centrifugal "gravity".
Anti-matter can do it rather easily (100x more efficient than the best fusion, at least). You could easily build something in the 10-100ton range using that kind of drive power (the issue with building small fusion starships is that unless we somehow can make very, very small fusion reactors the weight of the reactor will be rather large, thus, since 99%+ needs to be fuel, the total weight will be rather extreme).
Antimatter could give you 90% or so of light speed, and even allow you to stop at the other end and come back.
But producing that in usable quantities is somewhat beyond us. Not to mention the fact that our power production capacity is not really up to the task even if we could produce anti-matter at 100% efficiency.
And if people are afraid of nuclear reactors, what would they think of a flying bomb (either kinetic, or using the anti-matter directly, although that is less efficient actually) with a potential destructive power, if the ship weighs in a 10 tons dry weight, in excess of that of the asteroid that killed of the dinosaurs, or around 20M of our largest atomic bombs, to use a perhaps more graspable unit, one 1Mton bomb every 25 or so square-kilometer over the whole area of earth, or, you would have one on average 2.5km away..).
Also, even at 1%+ of lightspeed you will need some rather extreme anti-micrometerite screening, and self-repairing materials used in the ships, or it will be eroded away rather quickly.
I think we will be limited to our solar system for at least a few hundred years. But, that is rather large enough for a few trillion people, so that is not really an issue. If we decide to stick on the earth, however, I do not think things will end well.
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by instantaneously i meant transporting the whole thing at once instead of piece by piece or at the least increase the rate of transport(like pumping up the current), though indeed there still is a limit.
thats why what ifs and proposals gets denied 
Not that this is likely to cause anyone any insights into anything, but changing the current, or voltage, does not change the speed of signals moving thorough wires (unless you change it enough to break the wires, in which case it stops..).
It a rather constant .6-.9c depending on how the wire is made. Changing the wire can change the speed, but not even to 1c, not to mention over 1c...
