Ooooh. Oxygen and hydrogen. Just like the 1960-70's Saturn rocket upper stages, and the Centaur upper stage. And the Space Shuttle Main Engine (SSME). That's cutting-edge, fer sure.
People who are ignorant of propulsion often confuse "fuel" with "propellant". Propellants are oxidizer and fuel. You cannot "suck fuel from the atmosphere"; you can suck oxidizer. Air is 22% oxygen and therefore a pretty rotten oxidizer compared to liquid oxygen. And studies--repeatedly run since the 1960s--on sucking air and separating out the oxygen have shown that: (1) The equipment for doing so is incredibly heavy and (2) Any moisture in the air plays havoc with the heat-exchangers needed to liquify the oxygen. Oh, and (3) the energy required is considerable, which reduces the overall efficiency of the powerplant.
As for nuclear engines, they tend to have thrust-to-weight ratios in the "absurd" category. Whereas the SSME has a thrust-to-weight of about 70, nuclear rocket engines are in the range of 8-20. They would be suitable for an upper stage, but not for a booster. And an atomic air-breather was exhaustively studied in the 60's and 70's and it is simply a non starter. If you want, I'll provide gruesome detail.
--Boris