If you're playing the newer versions don't worry about the fighting skill until you have a solid base of weapon and armour / shield or primary casting skills. If you're playing an older version, fighting is super super super important. (It used to impact HP a lot more.)
You're better off focusing your xp into one or two skills max. You get the skill bonus the second it levels up, so don't waste xp by partially levelling skills.
Early on you want to avoid:
Snakes, Ogres, Orc Priest / Wizard, any named Unique. You can probably handle anything else in the game unless you're super weak. If you see several orcs, that usually means there is a priest around the corner.
Always ID your potions and scrolls. If you die with multiple un-ID'd potions in your inventory, you're doing something wrong. DCSS is pretty light as far as roguelikes go in terms of the ID game. You almost certainly won't die unless you're doing something stupid (like use-ID'ing potions with less than full health, in sight of enemies, in an unexplored area, etc). As soon as you have 3 of a potion, ID it. The one downside to this is mutation and cure mut, so some people will suggest you identify potions with scrolls, but I think for new players the very small chance of mut potions is far outweighed by the very real impact knowing what the common potions are will have on your success rate.
Felids are an easy way to win. They do teach bad habits though, so be careful with that. A good way to see the game though. And a lot of people (like me
((() die their first time in Zot, or a rune end, or Elf:5 or whatever. So having a run through with a Felid gives you a chance to see some of the dangers you may have to face down the road. Just try to play each life like it's your only life.
Don't walk towards enemies. Wait and let them come to you. You don't know what else is around that corner, and if you're exploring as you engage you may be in for a big surprise. Or, if you end up having to chase you could run into something or have to let the monster get away.