Picking up anything takes about 70 frames due to the slowness of the item window, and so, I would prefer a character who is (as said) as materially independent as possible, with no need to stop to pick things up repeatedly during the run, whether they be arrows or potions. Either a melee class or the mana-glitched wizard...
I played on with the mage to Act II start, and now I finally have the fear-inspiring Lightning Bolt. Well, it's not a let-down, although it's different from what I had expected. It's a "spray"-type magic like Burning Hands or Snowblind, although it has a lot bigger range (can hit outside screen), it homes somewhat to enemies, it stuns them and deals moderately nice damage too (72/sec) (and strangely, doesn't waste too much mana). It shares the same weakness as the other spray magics: it can only hit 1 target at once. So it's weak against groups. And in a TAS, where I expect you literally run past everything - it's possible so far, at least - you will likely not get this move until a lot later, if at all.
Fortunately melee is a viable alternative (melee attacks hit everyone in a group) since you can buy the Masterwork Great Sword of Speed (20-48) from the A2 shop (for a hefty 25198 gold though... potentially about 1000 gold less if you upgrade charisma during one of the level ups). It seems to be very effective against gnolls. It's by far the strongest weapon at this point of the game, although to get it in a TAS, you got to pick up some expensive magical items here and there to sell at the shop. Beating Xantham gives you a new bow, a sword and 900 gold which combine to about 5000-6000 gold already, so it's not that bad. For the record, this is a weapon I would pick up with the fighting classes as well. Although: there is a possibility that the sword is actually unnecessary, if later on you will get an even better one with less hardship (like from a barrel) and there aren't many mandatory enemies before that point.
For the Act I latter half... Magic Missile is a powerhouse I didn't expect it to be. At level 3 (taking 6 skill points to get there, which is exactly how much we can spare if we wan't Lightning Bolt at lv. 9) it deals 30 damage consistently if all 3 missiles hit, even to the Orb and Xantham, and that's a lot better than with any of the other more expensive missile-type magics at low levels. It also costs mere 4 mp per cast. However, there's a small cooldown after each cast which is a bit of a hindrance, but you can combine melee in these breaks for some additional damage.
We'll see how well one could fare with just magic missiles and the Great Sword as I progress into the mountains next.
EDIT:
So, the expensive sword is not really necessary after all, I think. There's only one mandatory fight in the forest, to get the cage key, and only one to three gnolls have to be killed. Sword might make it slightly faster, but if you had to go out of your way to gather money for it in the first place, it's probably not worth it. In the mountains there's 0 mandatory fights, although it's arguable whether you should grind slightly at this point. Magic missile works oddly well in the mountains for killing things 99% safely - the foes there are so big that it's easy to have all the missiles hit. You can effortlessly pick up expensive items from slain enemies (one particular enemy drops a sword that gives 4750 when sold with 13 charisma), and that might come in handy... I don't know what kind of cool stuff the act III store has to offer, but whatever it is, I'm sure it will be very expensive.
Once inside the mines you will become overwhelmed without something stronger. Lightning Bolt works like a charm, Missiles... not so. Trying to melee the drows seems slightly desperate, although it would be possible, if arduous, in TAS conditions.
EDIT 2:
After getting Lit. Bolt, the rest of the game was a breeze. After upgrading Lit. Bolt, it even gets an area effect so that it is not useless against groups. It does drain mana more than what is comfy, especially on low level settings, but that's what replenish pots are for (which, by the way, one probably should hoard from Act 2 or 3 stores). Now all we need is a decent grinding spot, and the overall strategy is set.
While the Act III shop has some intriguing items, at least a wizard does not need much from there, except possibly the +4 int amulet. I'm really torn between whether the character should do any melee later on in the game or not. There exists exploits against most bosses which makes them sitting ducks for your spells - running enemies can be tricked into harmlessly running towards you, never reaching their destination. Melee enemies can be fooled by going just far enough from them to stay out of their reach. They keep hitting at nothingness. Even the final boss has a severe A.I. failure if you just walk behind the staircase you came through - she tries to walk through it or something, and her projectile is the only threatening thing about her after that.
The elven warrior you unlock after finishing the game is an interesting case. He starts with burning hands and magic missile, making him a very viable early game killing machine. Alternatively, you can pump up his starting str to 19, unlike with any other char, and utilize his melee skills and be very effective in melee. I envision a run using him to start the game with him as a caster, later turning him to a fighter.