We have carried out experimental and theoretical studies of Penning ionization processes occurring in thermal energy collisions of state-selected metastable He*(2S) and He*(2S) atoms with ground state alkaline earth atoms X(X"Mg, Ca, Sr, Ba). Penning ionization electron energy spectra for these eight systems, measured with a crossed-beam set-up perpendicular to the collision velocity at energy resolutions 40-70 meV, are reported; relative populations of the different ionic X> (ml) states are presented and well depths D* C for the He*#X entrance channel potentials with uncertainties around 25 meV are derived from the electron spectra as follows: He*(2S)#Mg/Ca/Sr/Ba: 130/250/240/260 meV; He*(2S) #Mg/Ca/Sr/Ba: 300/570/550/670 meV. The spectra show substantial differences for the three ionic states X>(S), X>(P) and X>(D) and reveal that transitions to a repulsive potential -attributed to He#X>(P) formation -are mainly involved for the X>(P) channel. Ab initio calculations of potential curves, autoionization widths, electron energy spectra and ionization cross sections are reported for the systems He*(2S)#Ca and He*(2S)#Ca. The respective well depths D* C are calculated to be 243(15) meV and 544 (15) meV; the ionization cross sections at the experimental mean energy of 72 meV amount to 101 A s and 201 A s , respectively. Very good overall agreement with the experimental electron spectra is observed.