The Life Quests are perhaps the hardest to complete with only the Starter set, so don't beat yourself down.
It happens because it's more suited to high mana cap matches, rather than low ones.
Normally, I go for the Clay Golem, Divine Healer, and Peacebringer as my go to cards for matches of 21-27 mana, and play the cards you mention from 27 to 30, using the Shieldbearer as tank.
Doesn't always work, still. But the Clay Golem does help against the Magic spam of the current meta.