Probably not going to last that long in Stage 2 because I still only have a short sword and cloth armor with the shop selling an overpriced leather armor for 400 gold.
Hahah; you needn't worry much.
Skeletons drop weapons & you'll likely find better armor at one of the depths (probably Depth 7, or 8).
Just be careful in how you explore Depth 6; you'll want to prioritize finding the items at this depth while avoiding any enemy encounters (especially since you don't have better equipment yet), so you can trade up to any better armor/melee weapon you might find. And avoid Skeletons & Swarm of Flies until you have stronger armor to withstand their damage.
Once you have decent armor, you'll want to start farming Healing potions from Swarm of Flies, at Depth 7, where they spawn the most (Just remember not to farm too much, that your Warrior exceeds Level 12, when the flies stop dropping Healing potions).
Thank you and I'll re-read this next time I get past Goo. Sorry but I already resumed the game before I read this and got killed by a gnoll shaman at depth 7 but it happens. Already ran into a room with 3 skeletons and only just survived but after that the shaman killed me before I found anything more than a -2 cursed spear from a skeleton. They're more likely to be degraded/cursed anyway, so oh well.