It is usually better to stick with a promotion line that unlocks, e.g., ranged promotions or logistics/blitz (2 attacks/turn) or march (heal every turn). So for non-ranged units stick with the drill or shock lines (don't mix the two and don't divert to take, e.g., siege, cover or medic, unless you don't care about delaying march/blitz) and for ranged units stick with the accuracy or barrage lines until you can take logistics or range (you can take march afterwards).
I stronger disagree on melee units promotions. I never try to get march or such, the most important promotion on them is cover. Cover let them to survive after they attack, meaning they can pillage next turn and attack again. They never had health to do 2 attack/turn. Same try about armored units, but they do not have cover, so for them i try to get march. One attack and run why pillaging is strategy for armored units.