>>1178238space elevator to start with. we cant assemble the thing on earth and too many launches would be needed with rockets.
probably then need a railgun on the moon or mars to give some starting velocity so we can escape the solar systems escape velocity at earths level, which is high as fuck at over 40 000 meters per second. you probably will need rocket assist to actually get somewhere.
then for sustain once you get out to about pluto level you can probably switch on your main engines which are probably going to be magneto-plasma/Lorentz engines because at that point a high impulse will be useful despite low thrust.
then, you need to figure out how you will actually get people from point a to b, being do you sleep them, do you leave everything to be automated, do they just carry on normally.
lastly, you then need to have somewhere to go and you will need to store up the resources for that ship to last for the entire journey. there probably would have to be resources sourced from places within the solar system that aren't Earth