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The Tsiolkovsky rocket equation gives a general formula, applicable to any time of rocket that shoots exhaust out the back to accelerate in the forward direction, which can tell you the ratio of initial mass including fuel to final mass once fuel has been expended, given the values of the "effective exhaust velocity" (given for different types real and of hypothetical rockets here and here), the acceleration rate during the rocket burn, and the change in the rocket's velocity between the beginning and end of the burn. In this answer I did some substitutions and rearrangements on the relativistic version of the Tsiokolvsky rocket equation, to get a formula that would give you the initial/final mass ratio expressed in terms of effective exhaust velocity V, acceleration A, and distance traveled D between the beginning and end of the rocket burn (expressed in units where the speed of light is 1, like seconds and light-seconds):

The Tsiolkovsky rocket equation gives a general formula, applicable to any time of rocket that shoots exhaust out the back to accelerate in the forward direction, which can tell you the ratio of initial mass including fuel to final mass once fuel has been expended, given the values of the "effective exhaust velocity" (given for different types real and of hypothetical rockets here and here), the acceleration rate during the rocket burn, and the change in the rocket's velocity between the beginning and end of the burn. In this answer I did some substitutions and rearrangements on the relativistic version of the Tsiokolvsky rocket equation, to get a formula that would give you the initial/final mass ratio expressed in terms of effective exhaust velocity V, acceleration A, and distance traveled D between the beginning and end of the rocket burn (expressed in units where the speed of light is 1, like seconds and light-seconds):

But an antimatter rocket is probably unrealistic for a civilization that hasn't already begun making interstellar journeys, more realistic would be some kind of torch ship which has both high acceleration and high change of velocity, compared to either existing systems like ion drives (high change in velocity compared to chemical rockets, but very low acceleration so the time to achieve that change in velocity is large) or chemical rockets (high thrust but much lower change in velocity than an ion drive, for a given fuel mass). Aside from really advanced technologies like antimatter drives, the most likely technology would be some kind of nuclear drive; the chart here shows that the exhaust velocities for various types of nuclear fusion reactions as fractions of light speed, and the giant rocket engine list I posted earlier also shows a number of nuclear-thermal rockets that use fission (look for ones with 'NTR' in the 'code' column of the chart). That chart gives effective exhaust velocities in meters/second, but you can divide by 299792458 m/s to get the effective exhaust velocity as a fraction of light speed; I wouldn't bother with anything that has an effective exhaust velocity much lower than 0.004 times light speed (about 1.2 million meters/second) or 0.003 (about 900,000 meters/second), since plugging these in for V in the equation I gave while keeping the other values of A=0.00011776 and D=0.522 indicates a mass ratio of about 50 for V=0.004 (meaning you need about 49 tons of fuel for every ton of payload) and 186 for V=0.003 (185 tons of fuel for every ton of payload).

But an antimatter rocket is a pretty far-future technology, more realistic would be some kind of torch ship which has both high acceleration and high change of velocity, compared to either existing systems like ion drives (high change in velocity compared to chemical rockets, but very low acceleration so the time to achieve that change in velocity is large) or chemical rockets (high thrust but much lower change in velocity than an ion drive, for a given fuel mass). Aside from really advanced technologies like antimatter drives, the most likely technology would be some kind of nuclear drive; the chart here shows that the exhaust velocities for various types of nuclear fusion reactions as fractions of light speed, and the giant rocket engine list I posted earlier also shows a number of nuclear-thermal rockets that use fission (look for ones with 'NTR' in the 'code' column of the chart). That chart gives effective exhaust velocities in meters/second, but you can divide by 299792458 m/s to get the effective exhaust velocity as a fraction of light speed; I wouldn't bother with anything that has an effective exhaust velocity much lower than 0.004 times light speed (about 1.2 million meters/second) or 0.003 (about 900,000 meters/second), since plugging these in for V in the equation I gave while keeping the other values of A=0.00011776 and D=0.522 indicates a mass ratio of about 50 for V=0.004 (meaning you need about 49 tons of fuel for every ton of payload) and 186 for V=0.003 (185 tons of fuel for every ton of payload).

Looking it over, there are very few examples on the chart that have an exhaust velocity in the range of 1 million m/s or higher and have a high thrust in the thousands of Newtons range (necessary if you want 1 g acceleration); in fact it looks like none of the nuclear-thermal fission designs would be in anywhere near the right range, so a nuclear fusion drive (labeled either 'Fusion' or 'Pulse' in the 'code' column) seems to be the most likely alternative to antimatter, though near the bottom of the chart there's one called "NSWR (90% UTB) MAX" which turns out to be a nuclear fission based design using a nuclear salt water reaction, with this particular option assuming a very enriched uranium salt where "the 2% uranium bromide solution used uranium enriched to 90% U235 instead of only 20%". In this case the theoretical exhaust velocity would be 4700000 meters/second, and if you divide by 299792458 m/s you conclude this works out to V=0.0157, plugged into the equation that gives a mass ratio of only 2.7, or 1.7 tons of fuel for every ton of payload.

Looking it over, there are very few examples on the chart that have an exhaust velocity in the range of 1 million m/s or higher and have a high thrust in the thousands of Newtons range (necessary if you want 1 g acceleration); in fact it looks like none of the nuclear-thermal fission designs would be in anywhere near the right range, so a nuclear fusion drive (labeled either 'Fusion' or 'Pulse' in the 'code' column) might be the most likely alternative to antimatter. However, near the bottom of the chart there's one called "NSWR (90% UTB) MAX" which turns out to be a nuclear fission based design using a nuclear salt water reaction, with this particular option assuming a very enriched uranium salt where "the 2% uranium bromide solution used uranium enriched to 90% U235 instead of only 20%". In this case the theoretical exhaust velocity would be 4700000 meters/second, and if you divide by 299792458 m/s you conclude this works out to V=0.0157, plugged into the equation that gives a mass ratio of only 2.7, or 1.7 tons of fuel for every ton of payload. So, that could be a good option for a type of technology that fits the basic parameters and isn't as advanced as a fusion or antimatter rocket.