The post-main-sequence evolution of stellar activity and of nonthermal processes in solar-type atmospheres is studied through a detailed comparison of the current Sun (G2 V) with the very old solar-type star beta Hyi (G2 IV). Magnetically related activity decreases with age, and in very old stars one might possibly find the ''absolute minimum'' of stellar activity. In the solar galactic neighborhood, the closest single solar-type star, with an old age well-determined from evolutionary tracks, is beta Hyi (HR 98, HD 2151; G2 IV). Its successive atmospheric layers are analyzed in a series of papers, where this Paper I treats general stellar properties and the deeper atmosphere. Following a critical review of data from various sources, the age of beta Hyi is determined from evolutionary models to 9.5 +/- 0.8 Gyr, twice that of the Sun. Its proximity to the main sequence in the Hertzsprung-Russell diagram tells it originated from near the solar position of G2 V. Being the closest subgiant, beta Hyi is a bright target and has been observed under very high spectral resolution. A relatively high lithium abundance may be a signature of the early subgiant stage, when lithium that once diffused to beneath the main-sequence convection zone is dredged up to the surface as the convection zone deepens. Numerical simulations of the three-dimensional photospheric hydrodynamics show typical granules to be significantly larger (a factor of congruent-to 5) than solar ones. The photospheric pressure is smaller, thus limiting the flux density to which photospheric magnetic fields can be compressed. The lower surface gravity and density leads to greater granular velocities (a factor of congruent-to 1.5-2), since the same surface energy flux as in the Sun must be carried by lower density gas. Synthetic Fe i photospheric line profiles computed from these ab initio hydrodynamic models are compared to those observed at very high resolution (lambda/DELTAlambda congruent-to 200,000). The line cores indicate a stellar rotation v sin i = 2 +/- 1 km s-1, while the line wings suggest the presence of transonic or supersonic motions in the more vigorous granulation on this subgiant.