Well a couple of things, the major one being using 1 g acceleration to near the speed of light.
The amount of fuel, even using a nuclear powered vehicle, with an ISP far greater than we have today, would take an enormous amount of fuel. The mass of which then makes accelerating (and having the nearly same amount of fuel to decelerate as you near your destination) such a mass essentially impossible.
Note, nobody is going to fly to another star system except to land there. There would be no possibility of return.
Which means not only do you need the mass of the landers, but sufficient supplies/equipment to give the people landing on this new world, a chance to survive. The number of people sufficient to start a new colony would also be a major factor. Hard to believe you could do it with less than 100 people.
Considering how long the trip would be, and the mass of people, food, water and power generation, along with the descent stage and materials, the mass of said spacecraft would be huge. Which drives the mass of the propellent required.
Second problem is space is not empty, and at anywhere near the speed of light, no material would withstand the energy imparted from collisions even at space densities.
C/5 might be possible, but even then, going 4 LY would take more than several decades, and you wouldn't be going fast enough for time dilation to reduce the length of the trip.
As to communication, its not just the time it takes for a signal to reach its destination, its the amount of power one would need to send a signal that distance, which for the spacecraft at least would be highly problematical, to have both that much available power and an antenna large enough for the task.