I've been starting characters in various classes, in order to get some insight into their differences. I've learned a few things about getting them up to 6th level:
Archer
The easiest way to start an archer is to do the house quest. Set explore to running and tactics to berserker and take advantage of your prowess with whatever missile weapon you start with. Then try the barrow quest. Try to have arrow-making early. Turn off the automatizer to save the elven bones for later.
A hobbit archer is also a good choice, particularly as ammo can be made from the beginning.
RedNaga: "barrow quest" may be misleading to beginners (to which this article is most interesting anyway) - they could receive the wight quest and get confused - i think you refer instead to entering in the Barrow Down dungeon. Also for the automatizer: i use a rule that tell the automatizer to never destroy "junk" when playing an archer, since i know he'll get ammo creation eventually.
Eru Priest
Generally difficult and a bit unbalanced. I tried a human but lacked a distance threat for the house quest. A hobbit priest is a bit underpowered early due to the sling. With a dunadan, I could buy a bow and use that to get to level 2 in the house quest. I bought a cantrips book before entering the house for when I would pick up some spells. Then I increased my prayer high enough to be able to use manathrust and was careful about dealing with one threat at a time. I still die quickly in the barrow quest, so I haven't solved it completely--Eru priests are weaker than archers. The Mindcrafting skill is cheaper to use than spells, but is much less powerful. Try to take on one creature at a time if you have it. Have some sort of area attack by the time you do the barrow quest.
For a while, my dunadain priest kept dying at level 8, but then I decided to do a careful level or so of the barrow downs dungeon before taking on the house quest. That allowed me to get mindcrafting and manathrust before going into the house. He's up to level 14 now and has just finished the barrow downs dungeon. He still has to be a bit passive around orcs, kobolds, and the like, but he's advancing slowly.
Generally speaking, you will feel the lack of a distance threat acutely. You can't dive safely, even at normal rates, and you have to watch your mana reserves like a hawk since manathrust and the mindcraft spells are expensive and less effective than the elemental missile weapons in taking out higher level monsters. Your hand-to-hand skills will never be great, so you might think about increasing the number of blows you can land to make up for that. Since you should earn a lot of prayer points from your temple quests, you should limit your advance in prayer, but that means your associated spells will not advance rapidly unless you take on the temple quests quickly--dangerous. As noted above, unbalanced.
NeilStevens: I think manathrust is the single best ranged magical attack in the game. If you only get to have one, that's the one you want. Combine that with access to Divination, and an Eru priest is doing just fine magic-wise.
If you need more mana, adjust your skill point usage.
GreyCat: Hmm... mindcraft to deal with hordes of low-level monsters, and manathrust to deal with single big ones? Sounds like a plan to me. Of course, mindcraft won't be effective for offense until you get the skill up to level 25 or so. Until then, I guess you need to use manathrust and a weapon.
HarryErwin: I find a combination of Neural Blast and Pulverize works nicely, although I stick with Manathrust for intermediate-strength attacks. I start with Sense Hidden and shift to Precognition at level 5 for trap detection. Detect curses isn't particularly useful once pseudoID gets up a bit. I check my log after using See the Music at level 30, so I don't miss the random artifact. I do try to upgrade by weapons skills enough to get pseudoID on weapons and armor.
JasonStitt: Keep in mind that around the time see the music stars identifying items on the floor, potentially wasting artifacts, you have other options. The identify spell will start identifying your pack for mana rather than piety, and within a few levels know the music will *identify* your pack.
Mindcrafter
HarryErwin: I've been experimenting with Mindcrafter worshippers of Eru. The balance of skill points works better than for an Priest(Eru), and you can max Prayer and Mindcraft with less skill points as long as you do the Lost Temple quests. Mindcrafters seem to come out slightly ahead on other skills, too. A dwarven mindcrafter-Eru worshipper seems to be one of those minimaxed classes with a high advancement rate.
JasonStitt: Assuming you want 50 in both prayer and mindcraft, mindcrafters will come out 7 skill points ahead of priests no matter how many god quests you do. On the other hand, priests come out 12 points ahead getting to spell-power 50. Advantage for all three: priest by 5 points. Depends on how much of each of those skills you actually need, of course. The mindcrafter will also likely end up saving 1 or more points on magic device.
Ranger
Very much like an archer, but get your magic underway early, too. Try to have arrow-making early. Turn off the automatizer to save the elven bones for later.
Next
I try to get the ring of invisibility to allow me to deal with the mushroom quest peacefully.
Chatter
NeilStevens: My advice is to gain experience as fast as you can. For most classes that means killing a Crebain, then powering up Magic-device to kill big game with wands.
RedNaga: the house quest is good for any (well, almost...) character! With running and berserker tactics, even a magic-oriented character can kill enough novice rogues to get to level 2 or 3, where his spell become effective to clean the rest out! And if you like wandering the wilderness (i don't), levelling up there is an effective way of starting up your character with little risk.
ElIott: very true! I had a zombie hobbit warper (long story) enter the quest immediately after starting and after getting frustrated trying to kill them with a sling and his sad mana reserves ultimately resort to using his bare hands (no barehand skill OR melee weapons) on bersker/running to beat them to death. It worked much better than the sling or manathrust at level 1 with 6 mana.
GreyCat: One problem with "gain experience as fast as you can" is that if your equipment doesn't keep up with your level gains, you might not be able to handle the god quests when you get them. And you don't really want to delay them too long for fear of losing all those skill points.
NeilStevens: Only applies if you care about those, though, heh.
JasonStitt: This is probably more significant for melee types. If you have good spellcasting ability you just have to play more carefully until you get good equipment. And with a decent magic arsenal you can quickly dive deep enough to get it.
ToME Wiki