How do I survive as a spellcaster long enough to become powerful?

I've played almost exclusively magic users (although I tend to roll a bit of assassination in there as well), so perhaps my experience will be of use to you.

The biggest thing I can say is - exploit the enemy AI. They tend to be fairly braindead about how they assault you, and they won't open doors or use teleportation glyphs. One time I took a whole zoo down 2 or 3 monsters at a time by using small passages to keep them from surrounding me, and exploiting the fact that they have poor pathfinding. Typically, the enemies would rather walk against a wall than try to find a way around it. When the coast was clear, I'd open my door and walk to the end of the wall, which would cause a few enemies to spill over it. If I walked back into the room and waited a bit, I'd have a manageable clump of enemies to off before my mana completely drained.

I tended to hoard liquor, and buy it from vending machines when I could. However, you can also restore mana by just walking in circles, so if you get into a fight, make a few kills, and are tapped out, retreat. Close a couple of doors, and then you can recover. Knowing where a relatively "safe spot" is can make all the difference.

Skill-wise, I played mostly a mage with some support skills, and this is what I leveled early:

• I really like the Assassination tree. Most of the skills in here are passive, so they work regardless of your current weapon or mana and have no cooldown. Being able to stun an enemy in a bottleneck so that you can flee, or just do critical hits more often when you're low on mana, is a big plus.
• Get a pet to tank for you. Early in the Promethean tree, you get to summon a wyrmling. This summoned monster is an invaluable tank. Golemancy has similar "monster summon" abilities, if you prefer to have it even earlier.

The Promethean tree also has early-game area-of-effect and damage-over-time in the form of Dragon's Breath. If you lead enemies into a narrow hallway, breathe down the hallway, and then smack the closest one around with Assassination, the other enemies will wander about in the flame patches, softening them up for later. The occasional stun from Blackjack means they're not going to be getting that many hits in.

Crafting and item wise, I tended to have enough liquor to suit my mana needs, but you can also distill many types of liquor to craft mana or health potions if you have the necessary ingredients. In the early levels, when you find rusty equipment, you can grind it down to make one of the ingredients for a health potion for example. Similar rules apply to aluminum gear for making mana potions.

There's kind of an overwhelming amount of different foods. I tended to prefer the Cheesy Omelette, just for inventory conservation purposes. You can use the ingot grinder to grind most types of cheese, and add a single diggle egg with 3 stacks of grated cheese in the ingot press to create an omelette. As my inventory tends to overflow with diggle eggs and cheese, this worked well for me.

Gaslamp Games made sure that few if any Wizard skills had easy nukes on the first level. Promethean is the 'best', and it sucks. So if you want to play a Wizard and make it past level 1 without a lot of insanely careful clicking around, you have to have at least one solid non-Wizard skill that will take the pain out of killing those first dozen monsters. OR be willing to go 'gish' -- i.e. take a Wizard skill or two that make hitting things in the face a viable option. Staves is probably your best bet, and pair that with a skill that has either a 2nd level heal or a 2nd level pet (Golemancy, Fleshsmithing) so that you can continue safely hitting things in the face until you get a real nuke (Obvious Fireball, My Chemical Explosion, etc.)

Warlockery and Viking Wizardry also provide the necessary first-level offense, but taking Staves will make you significantly less squishy up front as well, which is a big benefit. You can also ace the first level almost single-skilled-ly with Practical Geology, which gives a HUGE +5 Melee Power as it's first-level spell. Sure, you won't crit or counter with it active, but +5 MELEE POWER -- who cares? :) For a Wizard who just needs to kill enough Diggles that his few cheeses will get him through to level 2, this is golden.

Finally, there's the 'Fleshsmithing Gambit'. With Fleshsmithing's first level spell, you get a pet -- but you need a corpse to animate as a Zomby. If you're daring and brave, go all Wizard and take Fleshsmithing (you'll love the heal later on), and challenge yourself to take on the very first mob you meet in melee -- then, if you live through it, you can animate it and have your pet Zomby(s) clear out the rest of the first floor for you, giving you easily enough XP to have Obvious Fireball or beyond by the time your pets become less useful.

I've got some more input on this...though I second that assassination is actually REALLY useful for mage builds.

To keep your mana up I also suggest the Blood Mage tree, especially if you are going to use the monster summoning abilities (and add the first level fleshsmithing ability to that list...though it requires a corpse). The trick to surviving as a mage is to not get hit, stay as far from the monsters as possible, hit them from across moats and such, use AOE spells to soften up targets. Oh, and don't get surrounded. If you find some enemies, then use your spells to grab aggro and then retreat to a place where you can fight them on your terms. And, although your mileage may vary, if you've snagged the free expansion pack you can also snag warlockery for that mana shield spell, very useful for staying alive.