Like I said, whatever works, whatever off the shelf commercially available nuclear reactor at the end of the 21st century, I admit I am not a nuclear engineer, but I know about nuclear power plants, and the Fusion program just seems to be soaking up money and their progress is so slow with them talking multiple decades just to build an experimental reactor the ITER, and multiple decades more to build a commercial power plant with what was learned. I think if we are to do a starship by the end of this century, it could only reliably count on atomic fission as its main power source, I've calculated by the way it would take 1000 metric tons of fissionables to light and heat a 500 meter diameter Island One Bernal Sphere habitat for every 1000 years of the journey, and at 300 km/sec, that journey to Alpha Centauri would take 4100 years, because Alpha Centauri is approaching us, so figure 4100 metric tons of fusion fuel for lighting and heating the habitat.
I think most people take a wait-and-see approach to fusion. If they get a reactor working for a year or two we'll have an idea what it would take, power-to-weight ratios, thermal efficiencies, neutron damage problems, and maintenance issues. Till then, it might as well be a warp drive.
But I also wouldn't design for a 4,500 year journey to the nearest star, for the simple reason that someone else could just devote a little more fuel to acceleration and get there in 500 years. That means that when your slow ship arrives, people will have already been living there for 4,000 years.
Even with a population increase of just 0.5% per year, it means that your ship's passengers will be greeted by 400 million descendants for every person who departed on the 500 year ship. But of course 50 years after the launch of the 500 years ship, somebody will launch a 100 year ship, and 50 years after it launches, someone will launch a 20 year ship.
Ironically, for a while ships from Earth will probably arrive at the nearest star in the reverse order that they launched.