If you REALLY want to dive into it there are a lot of good videos on youtube that go deeply into it. I have a background in astrophysics so I'll toss a few points out.

First of all space is massive. REALLY REALLY massive. Don't let small numbers like 4 light years make you think it is trivial. If the sun and earth were reduced to a distance of 1 inch the nearest star would be over 4 miles away. This isn't like crossing an ocean faster. Theories of spacetime manipulation (I assume you mean wormholes or "bubbles") are just pure conjecture. No evidence of such has ever been seen in nature and even in theory they require exotic forms of matter (such as negative mass) that are purely theoretical and massive (solar level) amounts of energy.

1. I want to get there within a generation. Therefore you must go at a significant percentage of light speed just to reach the nearest star.
   1.1. Energy costs grow ASYMPTOICALLY with relativistic speeds, not linearly. You'd have to carry so much fuel (fusion or fission doesn't matter) that you hit the rocket tyranny issue very quickly. More fuel to move requires more fuel which requires more fuel, etc. To move 1 kiloton of mass at 10% of light speed requires about as much energy as 2,000 Tsar Bombas, the biggest thermonuclear weapons ever made. Using hydrogen fusion it would require 1,440 metric tons of hydrogen at a 50% efficiency (very good) rate for each kiloton of mass.
   1.2. Solar power isn't an option. Chemical fuels aren't energy dense enough. Nuclear power helps but even that requires massive amounts of propellants, not to mention the radiation they produce. Matter-antimatter is the strongest but containment for decades is unlikely and the total amount of antimatter produced by all of our particle accelerators is about 20 nanograms. One glitch would cause the instant destruction of the ship.
   1.3. If you want to send people that means you are talking about many, many kilotons of mass. Most spaceship designs we've imagined go from thousands of tons to billions for multigenerational ships.
   1.4. At relativistic speeds even the vacuum of interstellar space, at about 1 atom per cubic cm, starts to resemble having a particle accelerator aimed at you for decades. Even small dust grains hit with tremendous energy. Light becomes blue shifted in front of you and more energetic. This would require even more mass for shielding. Magnetic shielding requires massive magnets and incredibly strong fields at those energies so even more fuel.
   1.5. If you intend to visit anything and not fly by it you now need DOUBLE (at least) the fuel and cannot depend on earth based schemes.
   1.6. Scooping up interstellar hydrogen for fuel costs more energy than it produces.

2. Ok, we'll go slowly. We'll putter along for maybe TENS OF THOUSANDS of years.
   2.1. Multigenerational ships now must be totally self contained with NO outside resupply, raw materials, energy, parts, etc. Absolutely nothing can be lost. Practical issues that exist regardless of the technology appear. Things break, things wear out. You have to have the means to manufacture your own equipment and fix those repair machines too. You have to be totally self sustained and we have never been able to keep a totally enclosed biological environment going for more than a few months.
   2.2. Sociologically you hit issues of who will lead? What are the ethics of knowing generations will be born into a ship they can never escape on a mission they never chose? What if things break down sociologically like they have on expeditions and remote bases on earth? After thousands of years they may decide they have had enough of being isolated.
   2.3. Fast or slow you've left the protection of earth's magnetic field and even the sun's heliosphere. You are now subject to the constant barrage of high energy radiation permeating space. Cosmic rays that can punch through 20 stories of concrete cannot be blocked by any reasonable shield. They will constantly cause biological, especially genetic, damage. Slap on more shielding? Ok, that's more fuel.
   2.4. Communication with earth becomes a year long process or more. Anything you ask will take at least 2 years to get a response at 1 light year.
   2.5 The fastest object we've sent out so far is the Voyager. It used gravitational assists due to a rare planetary alignment. At its speed it would take ~75,000 years to reach Proxima Centauri.

3. Forget sending people, we'll send robots!
   3.1. Sending gram sized probes with massive solar sails has been proposed. You are now trying to cram all of your tech into something the size of dice.
   3.2. The solar sail would need to be huge, thinner than a human hair, but still able to handle the intense power of gigawatt lasers from earth without deforming. The lasers would have to produce energy equivalent to that produced by the entire USA.
   3.3. It wouldn't be able to stop, it would be a flyby mission with less than a day to gather any info.
   3.4. A tiny object would have to transmit this back to earth somehow and be picked out of the noise and radiation of the star it is visiting. Like detecting a match on Mars while staring into a searchlight.
   3.5 It would also be subject to the barrage of interstellar atoms, radiation and occasional dust particle.

I'm sure I'm leaving some points out but these are the basic issues people have run into analyzing it. Many of them are fundamental to spacetime itself and cannot be "out teched".