What troops and strategies should I adopt in order to raid for resources with low cost?

The most cost effective troops to use in raiding enemy bases is the barbarian and archer combination.
These two are the most low cost troops you have and takes only a few seconds to train which makes it both time and cost effective.
The basic strategy to use is to deploy your barbarians first then followed with your archers.
The defensive structures like the mortar and wizard towers will target the barbarians because they will be the first line of your offense troops and these barbarians need to come close to the structure they want to attack in order to cause damage to them.
The archers on the other hand keeps their distance from enemy buildings and can attack from afar making this type of strategy effective and keeping the troop cost low.