I find that wars before Nationalism tend to move too fast for bombardment units, so I don't really build them. I acquire them at the end of a sword.
Once you get to Riflemen/Cannons & definitely Infantry/Artillery they become less of a luxury and more essential.
I started a war with the Japanese, and had my two Infantry Army Groups attacking one from the Northern and one from the South-Western Border of my land. They each were split into three Divisions of 12 Infantry supported by 12 Artillery, so that’s 72 troops in each force! (I am a very organised war manager  ). I also sent my remaining Sipahi force of around 80-90 sipahi through the middle of the Japanese in order to cut off their forces into two theatres, thus being able to take the northern one and isolate the southern.
Anyways, I’m getting off track. After a few turns of war I’d captured about 15 cities, and secured all my war aims. My Northern army had lost 1 infantry, my southern had lost 3 (all whilst holding cities) and my Sipahi had lost 50% of their number as Samurai, Cav’s & Inf took them down. Although Sipahi are awesome and fast, in the Inf/Art stage of the game they are easily decimated by their attacking prowess.
So yeah, in answer to your question, against unprepared computer, Artillery+Infantry will cause them a lot of problems if used patiently.