Marching tech increases the speed at which you travel the map as well as the battlefield and also is used for determining which units move/attack first in battle. Shooting increases the attack range of all units. Both of these techs are fairly important for a cav/arch army, you should be prepared to upgrade them both to max level.
How to counter Inf / Cat army with Cav / Arc? Both have same speed and techs. Please layout ur expert tactics n battlefield moves and which unit attacks which attack.