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You cannot avoid being pounced on by spiders, werewolves or ogres. Therefore, a high armor rating becomes key to your Dragon Age Origins solo strategy. High armor ratings reduce most pouncing damage to 1. Also, high armor helps in just about every battle. This requirement leads us to the Arcane Warrior that can wear heavy armor and cast several armor enhancing spells. Although armor is most important, we will not ignore defense.
The Rock Salve and Incense of Awareness help boost armor and defense further and are important items in the beginning parts of the game. Pick up any you can find in your travels. Purchase the recipes in Lothering. The Rock Salve will require 2 Deep Mushrooms and a distillation agent. For the Incense of Awareness you will need Lyrium, Deep Mushroom and a Distillation Agent. You will be able to make these potions once you reach level 2 in Herbalism.
Heavy armor increases fatigue for activated spells (e.g. healing, fireball, etc), but NOT sustained spells. Therefore, there is a lot of focus on sustained spells in this strategy (see spell list below).
Sustained spells are also great to cast after casting a few activated spells (like Fireball). Since sustained spells affect your maximum mana, but doesn’t cost anything, you effectively get the sustained spell for free. However, since casting a spell takes a few seconds, it is good to keep a few sustained spells on all the time. The best choices are - Rock Armor, Arcane Shield, Shimmering Shield and possibly Miasma. Then cast Death Syphon and/or Combat Magic in the middle of the battle if needed.
Lesser healing potions are a cheap and fast way to replenish health. Later in the game, casting Heal (or other healing spells) will cost too much mana since the fatigue will be high.
Two levels of combat training is useful to prevent spell interruption and for some mana regeneration.
When you are playing Dragon Age Origins solo, you should do as many side quests as you can for experience and gold.