There are also a number of solar sail spaceships proposed where massive lasers are used to direct concentrated laser light at the spaceship from our solar system. Of course, the passengers would have to rely on someone remembering to turn on the deceleration beam in time.
Project Orion is possible with 1950's era technology and the basics of the propulsion and the necessary shielding have been tested. Project Daedalus is dependent on acquiring Helium 3 and on research into hot fusion. Project Medusa requires a large solar sail of several kilometers so that the nuclear blast can be a safe distance from the sail, this may require carbon fibers for the strength.
The asteroid ship requires a massive drilling effort and a carefully planned expansion of the asteroid but a version where crowded habitats are just dug into the asteroid by conventional means without trying to make a large internal cavity could be done with existing technology.
The solar sail requires large lasers and power sources to be built perhaps on Mercury and large lightweight sails, most certainly with carbon nanofibers to be made.
Antimatter has the problem of creating or collecting the antimatter with the most likely source being anti-protons captured by the Earth's magnetic fields and then there is the problem of storage, anti-electrons all repel each other, anti-protons all repel each other so you have to combine them to something charge neutral like anti-hydrogen but once they are charge neutral, you can't keep them from colliding into normal matter such as their container. Not easy problems to address. Both fusion and anti-matter are improbable with our current technology.
I'd say the most likely as far as possible ships with today's technology, would be a scaled down asteroid ship without the internal cavity, then the Orion. The Medusa ship with technology that is likely to occur and Daedalus, the solar sail and the full scale asteroid ship for technology that are unlikely occur or require too great a scale.