Well, the big thing to remember is that you don't have to explore a branch to its end, just 'cause you're in it. As a general rule, you'll want to explore the dungeon until you run into the lair, which you explore to the very end -- or until something vicious (uniques, death yak swarms, etc) shows up -- or something dangerous blocking your way further into the dungeon. Once you've cleared out the lair and possibly the orc mines (and
maybe parts of elf if you've got decent MR and rF+C) and gotten as far into the main dungeon as you safely can,
then -- and pretty much
only then -- do you start testing the waters on the rune branches.
Even with cleaning out rune branches, you don't attempt the rune until you've explored pretty much everything else you can to the fullest extent you're able, at least until you're seriously familiar with crawl and what you're able to get away with.
I'm certainly not, even with a win under the belt, and so everything possible gets cleared out before any attempts on rune vaults. They're pretty much specifically set up to wreck you if you attempt them as soon as you possibly could -- and so you don't, until you're better prepared.
Do not be afraid to run away and go do something else. Just because things are going well does not mean they will continue to go well. You will run into situations you cannot overcome with your current resources, at which point you either go away until you
can or you die. The former choice, cowardice, is preferred

Getting used to when you go to certain depths and branches is definitely one of the mid-upper level techniques of Crawl playing, though. Certainly takes time to get a feel for it.
Re: Wand stash; branch ends are basically the entire reason that you're stocking those things. Next time, if you've got wands in your stash when you attempt to take a rune vault, go back, pick up the better ones and then use them. You could have dumped most of your scrolls (ID, enchant, fog, etc; the ones that wouldn't have specifically helped you survive.), some of your potions (Agility, berserk rage), and most of your food (Sprig wouldn't have needed more than two rations to clean out a rune vault and get back to the stash) to make room for them. Swapping the poly wand for a higher-tier damage wand (especially fire or lightning, in the pestilence case) would have been a good idea. Definitely should have kept the better rods, whatever they may have been, around. The main point of running a Nemelex artificer is to use those rods to pump evocations through the roof and get ridiculous effects from the cards your dungeon vacuuming is producing.