Grissenda
Grissenda is your most well rounded companion (and my personal favorite). Sturdy, dependable, simple. You can recruit her by gallantly charging a ghost to retrieve a family heirloom. You can build her as a Shield-Maiden, and bravely cower behind her wall of steel (she doesn't mind). Lower DPS, very high armor and health. This is a fantastic option for ranged builds, or melee builds with very high DPS that are more fragile. You can also build her to wield Two-handed Weapons. This will greatly improve her DPS [Damage per second] at the expense of durability. A great choice if you are playing a build that can take some hits too. Many find Grissenda the simplist companion to use, as you don't need to worry about mana.
Hirge
Hirge is a healing tank. Lowest in DPS, but she can be well-nigh indestructible. You can recruit her by braving a deathtrap dungeon to retrieve an important holy relic. She can be a fantastic focused Healer. The AI for her Heal Wounds spell is very good, and she will do her best to keep you and herself alive as long as she has mana. You can also turn her into an Immortal Tank, investing into Intervention, and as long as you have mana potions on hand, she will survive. It is *not* recommended you put any points into Arbenos' might. Her AI is very poor with it, and she burns mana very quickly. Sadly, you will be unable to convince her that a goblin is not a worthy enough foe to burn might on. Many find Hirge is the easiest companion to use as a beginner.