As to the most common types, in the infantry artillery category the most common was the 7,5cm le IG 18 and the 15cm s IG 33 which were used at company and battalion level to provide close fire support. In the field artillery category, generally at brigade or divisional level, things become slightly bewildering as no single standard gun was adopted; instead one would find a great deal of diversity between divisions and even between artillery companies. On the whole, however, the 7,5cm leFK 18 represented the light field artillery in most infantry divisions while the 10,5cm leFH 18 (howitzer) and its various upgrades were the primary medium divisional field piece. The companion piece to the latter was the s 10cm (actually 10.5cm) K18, a field gun whose higher muzzle velocity gave greater range than the same calibre leFH18. The final member of the field piece category was the 15cm s FH 18 and various upgraded improvements. This provided medium range heavy support fire and were organized along with the other medium field pieces at divisional level.
A very laudable attempt was made to standardize a gun which would have been suitable for both anti-tank and field gun serivce and the result was the 12,8cm K44. Development came much too late for service issue, although a small number reached the front on improvised carriages.
Heavy artillery, which fell under control of Corps level HQs, was represented by the 15cm K18 and 17cm K18 Mrs Laf long range guns, and the 21cm Mrs18. Attempts to replace these and a mix of captured heavy artillery with a standard 24cm gun resulted in the 24cm K L/46, but in the event production was very limited and only one battery of Arttillerie Regiment 84 was equipped with them.
The 8,8cm Flak 18, 36, and 41 represented the divisional and corps level AA outfits, while the larger 10,5cm and 12,8cm FlaK guns were mostly employed in static limited mobility units for area defence. These guns, 8,8cm and up were under Luftwaffe, not army control, and although they could and often were pressed into service as anti-tank weapons and occasionally as field guns, the Luftwaffe took a rather dim view of this as it took them away from their primary role, resulted in more rapid wearing out of barrels, and frequently exposed both guns and crews to enemy fire.
The various AT guns were fairly well represented by the 3,7cm PaK 36 (for all intent and purposes obsolete by 1940), the 5cm PaK 38, 7,5cm PaK 40, and 8,8cm PaK 43, and 12,8cm PaK44 (which eventually became part of the 12,8cm K44 program). There were also a wide number of enemy AT guns pressed into German service as stop gap measures and a variety of taper bore type AT weapons (at least until Hitler's order to conserve Wolfram for machine tools instead of employing it as penetrator cores required by these super high velocity weapons).
Of the various PaKs, only the 7,5cm, 8,8cm and 12,8cm could really be considered powerful enough in terms of the destructive power of their HE shells to be considered for field gun use, but they generally were unsuitable for this role as their high velocity and low trajectories made them distinctly direct fire weapons and they usually did not have field gun type sights for indirect fire. This is not to say they were not pressed into such service in emergencies, but their use as field guns was limited. As a rule, such guns are not as efficient in an artillery role as they are in their AT role. Among other things, their gun carriages are not designed to give the same amount of elevation as a deidicated field gun of similar bore size, thus their maximum range is often somewhat less. Besides, although HE shell was provided so the guns could defend themselves from enemy infantry or engage soft skinned vehicles, the majority of ammo produced for them was AP as befitting their role.
Perhaps, in closing, a word on the terms field gun and howitzer is called for. Generally speaking a field gun is a fairly long ranged weapon firing at moderate velocities and relatively low trajectories. Howitzers are lower velocity weapons which lob their projectiles at the enemy at high degrees of elevation. This makes howitzers ideal for firing at targets hidden behind hills or other terrain features. If you need long range you bring in the field guns, if however you need to engage an enemy screened by intervening terrain, then you give the howitzers a call, hence the mix of the two types in each of the in the light, medium and heavy field artillery categories. Today, there is less specialization in artillery and the tendency since 1945 has been to produce single designs to fulfill both low angle and high angle bombardment requirements