I'm not a really super player and I tend to over-favor gear rather than spells, so I rarely have more than level 6 spells (except as an all-out conjurer blaster sort). More often, I'm just trotting around as a fighter sort with some hefty weapons and a few level 1-3 spells. While you sometimes just get a particularly awful sequence of rng with the pan lords, it's still generally quite doable.
More or less what Siegurt said, but especially this:
A lot of the time it's simply a matter of providing the least opportunity for being ambushed, for each floor, figure out where the closest staircase is, and beeline for it, digging paths if they will save you more than a small number of steps.
Save wands of digging for the ascent whenever possible. I generally only use them for blasting grates, transparent rock and statues (when they block shops or other important stuff), and (mostly) for the ascent. Some games produce so many that you can use them much more liberally, but don't bet on it before you actually see heaps of charges. 15 or 20 charges is a decent minimum for quick ascent I'd say, but it's much nicer to have a lot more.
As always, knowing the mobs inside and out makes a huge difference. I don't know all of them down to the fine point stats and for the "extreme" combo situations the ascent can put you in after multiple encounters, so once in a while I still get shocked. But I try to LOS or else engage asap with anything that has torment, mutate, or a particularly
serious ranged ability. Nastier summoning or disabling sort of mobs are also worth eliminating fast, if they can pump out anything your'e still vulnerable to. Other than that, try to follow the narrower paths to the nearer stairs up. If you come onto a level far from all of the stairs, it's sometimes good to either go back down -- that's IF there's any other stair choice nearby on the previous level -- or even read teleport and hope you land somewhere better.
Ranged weapons are very strong in the game, so having a very well enchanted arbalest, longbow, or white upgrades along those lines can often be competitive. Also don't forget to check the mobs for low evasion and prefer to keep right on shooting low EV ones at point-blank. Also if you can get the Portal Projectile spell up. With that spell, you can smite bomb targets behind enemy lines maybe before they're ready to attack you. The spell also helps accuracy generally if I gather correctly. You might not hit quite as hard per shot as high-powered AOE conjurations, but hitting stuff "well enough" or "fast" at a distance is still valuable. Just don't carried away -- only shoot what's really going to be a PITA if you don't preempt it soon. Otherwise, keep on moving.
On fighter types with only 3-4 runes, I find the spell game a mixed bag. It depends a bit on how much Int your artifacts add, what mutations you get slapped with in Zot etc., and even what species you play. I still haven't learned to Passwall or to use Summon Butterflies consistently. And it starts to get to be so many schools of spells if you do all of the handy possibilities. Blink can be
extremely useful. I don't so often get around to all the others. Many of them
can be strong, but they take specific situations or practice. A few slots of stored evocables may do a lot of the things you'd otherwise want spells for: teleporting, blocking LOS, summoning temporary block/distraction minions.
Nets are awesome if usually limited availability (and some things are just too big). As usual, don't be too afraid to read Teleportation early if things look very dicey. Or maybe dig yourself a sheltered path around the edge of the situation/map if you have enough of a head start, have wand charges and a touch of space to dig through, and aren't getting smited too much getting started!