The smallest planet you can probably maintain an atmosphere on for gigayears of time is probably half to a third of an earth mass (barring the effects of geology). That gives you an escape velocity between 70 and 80 % that of here given similar composition and no thousand km thick hot ice layers or anything.
EDIT: If you assume an escape velocity of Earth’s and a specific impulse similar to a Merlin engine and ignore all gravity drag and atmosphere, using the rocket equation an SSTO to LEO requires a fuel to payload+structure mass ratio of at least 12.0. If you assume an escape velocity of 75% that of Earth, it requires a mass ratio of at least 6.5. Probably doubles your mass to orbit per unit fuel. If you have an escape velocity of 1.25x that of Earth, your SSTO requires a mass ratio of 22.4. Mars, by comparison, reads as a mass ratio of 3.1 under these optimistic assumptions.
Of course staging improves all of these numbers and squishes them together some, as does using better fuel than kerosine, while dealing with an atmosphere and gravity drag and propellants worse than kerosine makes things much worse. For a reality check, existing real multistage Earthly launch systems I just quickly looked up have mass ratios between ~35 and ~15 (though the 15 includes the total mass of the space shuttle not just the payload, while the upper stage is not included in other higher numbers for other systems).
The smallest planet you can probably maintain an atmosphere on for gigayears of time is probably half to a third of an earth mass (barring the effects of geology). That gives you an escape velocity between 70 and 80 % that of here given similar composition and no thousand km thick hot ice layers or anything.
EDIT: If you assume an escape velocity of Earth’s and a specific impulse similar to a Merlin engine and ignore all gravity drag and atmosphere, using the rocket equation an SSTO to LEO requires a fuel to payload+structure mass ratio of at least 12.0. If you assume an escape velocity of 75% that of Earth, it requires a mass ratio of at least 6.5. Probably doubles your mass to orbit per unit fuel. If you have an escape velocity of 1.25x that of Earth, your SSTO requires a mass ratio of 22.4. Mars, by comparison, reads as a mass ratio of 3.1 under these optimistic assumptions.
Of course staging improves all of these numbers and squishes them together some, as does using better fuel than kerosine, while dealing with an atmosphere and gravity drag and propellants worse than kerosine makes things much worse. For a reality check, existing real multistage Earthly launch systems I just quickly looked up have mass ratios between ~35 and ~15 (though the 15 includes the total mass of the space shuttle not just the payload, while the upper stage is not included in other higher numbers for other systems).