If we wanted to get to another planet in our solar system, we would likely use two types of rocket. One would travel very slowly, taking with it all the heavy equipment. The second would travel much quicker, taking the people, and meet up with the first at the planet. This is the method that NASA will likely use to get people to Mars. This is because there is a lot of radiation in space, and we want people to be exposed to that for as short a time as possible. It wouldn’t affect equipment however, so that could take the cheaper, slower option.
How big would the rocket need to be? Well, to get people to Mars, the rocket actually wouldn’t have to be much bigger than what was used to take people to the Moon.
If you want to get to a planet in a different solar system… we don’t really know how that could be done. The distance between stars is immense, and even travelling close to the speed of light, most stars would take several generations to get there.
If we were to make the journey, we’d have to abandon rockets, and find a better form of propulsion. NASA are actually funding some research into warp drives, which could travel faster than light! However, at this point the research has not shown any promising results.