Whenever I think about creating a spellbook for a specific Mage, I focus on that Mage's special abilities. In the case of the female Warlock, you can see that Curses, Burns and Demons are her friends. In her case, there needs to be some kind of balance between these in order to make use of all of her abilities. So, in general, think diversity.
You may find yourself going with fewer Demons if you instead have Sersiryx and a few extra curses and fire attack spells for him. While he seems to be fairly popular in games that I've watched and played, I eventually removed him from my book because I wanted two to three extra Demons and/or additional support spells.
This Mage has some equipment that synergizes well with her special abilities, and since she is trained in Fire, I usually put in a Battle Forge for mana generation and action advantage (for as long as it lasts). After getting my mana depravation under control, I focus on getting out some Demons.
Perhaps the biggest decision that you will make is whether you go with one or both of Gate to Hell and Pentagram. These two spells are significant in terms of both spellbook point cost and how you will play your position. Some people hate Gate to Hell. I've used it with some mixed success, however, and I'm not opposed to putting it in my book. If I do, I generally also add Cerberus to guard that zone.
Other than some Walls of Bones and a Wall of Fire or two, there are very few conjurations in my book (other than already mentioned), though I also have both a Mana Crystal and Mana Flower... and like to play none, one or both depending on the specific opponent Mage / strategy that they play.
In choosing your Demons, I'm a fan of getting a mix of Flame Immune and Flame-2 types due to the attack types. The immune ones have flame attacks (as does the Mage), and if you go only with those, you can end up trapped behind Walls of Earth if you aren't careful. Note that Sersiryx does not fly, and he might need some support if you use him.
Speaking of flying, Adramelech is a huge investment and most players will have a "solution" for high level creatures like him. It probably is worth it to include one or two Blood Demons, however. Whether you go higher or lower level Demons is up to you, though while I like having one Dark Pact Slayer, most of my Demons are 12- mana cost. I do this to get more attacks with general buffs.
While I agree that mana supply may be an issue if you don't purposely save it from time to time, I do think that this Mage has to have one or more Drain Life/Souls for use in keeping your Mage alive. Healing is out of school, so it will be difficult to gain healing through other incantations. (I do like the Healing Wand with her, however.)
My choice of incidental equipment (other than those obviously beneficial to her), I tend to go with the Elemental Cloak (especially if Gate to Hell is in my book) and/or Cloak of Shadows, Eagleclaw boots, Leather Gloves, and Veteran's Belt. Suit your own tastes there, I guess.
On your thoughts about Ignite and Combustion... these have their uses. Note that, even with Adramelech's Touch on your opponent, it can be hard to put more than a couple of Burns on a good opponent at any time. Spells like Renewing Spring and (especially) Geyser can put them all out in a hurry. The way to get more than one burn on a single creature using Ignite, by the way, when the opponent is not a solo mage, is to put a burn on a guard or other nearby creature and then shift it to the Mage at the end of the Mage's action.
Hope this provides some insight for you.
EDIT: My single favorite spell to use with her... is Hellfire Trap, by the way. Combine it with Teleport Trap if you put one in, and you can bounce a target around from trap to trap. I did this once after force pushing the mage through a wall of fire... after the Ignite and Force Push, I remember that the enemy mage had quite a few burns on him. (This is where I was taught the utility of having a Geyser in one's book.)
