Denver International Airport: Rent a car; it is the genuinely practical option, not an airport-transfer fantasy. From the west side of metro Denver, Salida is about 2½ hours in good conditions; allow roughly 3 hours from DEN after collecting the car. The usual approach is south via US 285 toward Poncha Springs, then into Salida. Cost: a rental-car day rate plus fuel; there is no useful rail link or frequent airport bus to Salida.
Colorado Springs Airport: Rent a car and take the highway west/southwest toward Salida; Colorado Springs is roughly 100 miles east. Plan about 2 hours in clear weather, longer in winter. Cost: rental-car day rate plus fuel. This is a sensible gateway only if the flight is materially cheaper or you are already visiting Colorado Springs.
Pueblo Memorial Airport: Rent a car; Pueblo is also about 100 miles east, with a drive of roughly 2 hours in normal conditions. Cost: rental-car day rate plus fuel. It has far fewer flight choices than DEN, so do not choose it expecting a seamless transit connection.
Harriet Alexander Field / Salida Airport: Useful for private and charter aviation only; it has no scheduled commercial service. From the field, downtown Salida is a short drive. Arrange a car or pickup in advance rather than expecting a taxi rank.