Typically, VSWR = 1.92 (or equivalently a -10 dB reflection coefficient) is considered in most references. More recently, in the scope of small antennas, - 6dB has taken the lead in this role, since small antennas are naturally less efficient and thus harder to provide resonance behavior. Regarding radiation efficiency, if your antenna is large, it is expected to present high values (over 90%). In the small antenna world, 40 to 50% is usually taken as acceptable goals in the design phase.

VSWR should be

Theoretical limits for the radiation efficiency are 0 and 100%. A good design should give values near to 100%, or near to 0dB. The smaller the values the antenna is less efficient.

The VSWR is quoted to be less than 2 for acceptable design. At resonance the VSWR should be smallest among other values.

Maximum eficiency of radiation can go upto or above 90%

The VSWR can be below 1.5

S11 should be -10 or less (i mean -15, -20,..) so -10 is the poort power transimitted 30% is reflected if it is less it is better. VSWR in applications like mobile communications , the Base station give an alarm if VSWR = 1.5~2 so if it is between these values the systme still operating but you can expect fulldown, so it is better to keep the VSWR < 1.5 but if it is

the perfect efficiency is 100% (there are no losses) but a value of 0.75 can be acceptable. For VSWR the perfect and theoretical  value is 1 (we use the parameter VSWR 2:1 to indicate the range where the VSWR is between 1 and 2 (it must be for the whole band of your application). the most used is the -10 dB bandwidth (it's the criteria used by IEEE and most of telecoms regulators)

achieving 100% radiation efficiency is always the goal of every antenna designer. But most practical cases achieving this is not possible. number of factors are responsible for this. As per your question, Its better not to keep the lower limits of radiation efficiency in your mind. whatever antenna you design make sure that it achieves higher values of radiation efficiency.

regarding vswr, the vswr value of 2 given you a reflection coefficient value of -9.54dB (nearly -10db). So workout your design such that it achieves less than 2 vswr value, which is most acceptable