Limitations of Long Distance Space Travel:
Gravity - Our bodies are designed to be under the weight of gravity. Every single one of our organ systems will shut down if we spend twenty or thirty years in space with no gravity. The lack of gravity also makes exercising all of our muscles very difficult. Forget a muscle group and it will atrophy so badly you won't be able to use it. The best short term solution is special exercise equipment, but there is no long term answer
Speed vs. Weight - long distance space travel requires tons of food, water, oxygen, and fuel. All of these things have weight. The more weight there is, the more energy it takes to move the spaceship (and the more energy you need, the more fuel, and the more fuel gives more weight, which means you need more fuel) There is no solution for this. The best idea so far is to use solar power to cut down on the amount of supplies you need to take (but you can't stay within the range of a star while leaving the galaxy or the solar system for that matter)
Speed vs. Time - There is no way to travel faster than the speed of light, it would take an infinite amount of energy. Humans have about 70 useful years of life where they can operate the spacecraft, meaning if you go slow, you can't make it out of the galaxy in the lifetime of a human. Cryogenics is a long way off, despite what anyone tells you, but that's the best hope we have.
Let see...
Gravity : what about huge ship with rotating part... simply the centrifuge forge who replace the gravitation force... problem solved !!!
Speed vs weight : in fact, it is the acceleration who need energy... once you have reach the desired speed, you can stop the motor and you will continue to flight in the space at the same speed... for between star energy, why not a nuclear reactor ? Actual one based on the fission or future potential one based on the fusion... About food, water and oxygen, it is only a scale problem... something big enough can host a full mini ecosystem... remember, in chimie, all is about stranformation, nothing is created or dissappear... human transform oxygen in CO2 but plant transform CO2 in O2 and carbone... we can eat plant and our toilet residu can be used for feed plant... Urine is already recycled now for make drink water... problem solved...
Speed vs. Time : again a size problem... a ship big enough with enough people can reach any place in the universe... don't need to be the same people at the arrival that these at the departure... nothing stop human to procreate in space... the future of space is not cryo but more some generation ship...
Point is that for interstellar travel, we need to see it big... very big... so ship will be impossible to launch from earth due to the mass... best way and the more economical is to build in space and use material from the moon ( due to low gravity, it is cheaper to launch something in orbit )...
Machine are not a solution for far exploration... first, there is the delay for give them order... same at the speed of light, it already ask a lot of time for communication between the moon and the earth... so, difficult to give a real time human reaction when needed...
So, what is needed is not a new landing on the moon but a permament base on the moon... a industrial base who extract material and build what is needed for explore other planet and maybe later, explore the galaxy...
In fact, explore planet is only a preparation stage of the galaxy exploration... some can say that it is not needed, some other will say that robot can collect the needed info... when in fact, the real goal is to colonize other planet outside our own solar system... if humanity don't destroy itself, soon of later our planet can be hit by a huge asteroid who destroy all life on earth... people living on Mars will be the only survivor of the humanity... more, a sun is not eternel... if humanity wish to survive, soon of later, we need to escape our solar system and find a new homeworld before our sun is not more...
About the "70 useful years of life where they can operate the spacecraft"... i forgot to mention that time is not something fixed... more fast you go, more the time dilatation is affecting you... by example, if a ship travel around the earth at very high speed ( near the light speed ) during 10 year ( time on the ship ), for a observer on eath it can be 100 year passing or more...
A little quote :
Time dilation would make it possible for passengers in a fast-moving vehicle to travel further into the future while aging very little, in that their great speed slows down the rate of passage of on-board time. That is, the ship's clock (and according to relativity, any human travelling with it) shows less elapsed time than the clocks of observers on Earth. For sufficiently high speeds the effect is dramatic. For example, one year of travel might correspond to ten years at home. Indeed, a constant 1 g acceleration would permit humans to travel as far as light has been able to travel since the big bang (some 13.7 billion light years) in one human lifetime.
Funny, 1g acceleration resolve the problem 1 and 3 directly !!!
About speed, high speed can be reach too... actual ion motor have very little trust ( acceleration ) but can work a very long time with very little use of energy... same with a little acceleration of 1 m/s, a motor working one year will lead to a final speed of 31536 km/s... and since the escape velocity of the milkyway is only 525 km/s...