If you don't mind me interjecting - what would be the minimal setup to make visiting Skull Caverns worth it? Not trying to go deep, just to get something useful (preferably some iridium) out of the visit. The detailed plan of attack seriousfarmer provided is fantastic, but I have almost none of that (gold pickaxe, a few bombs, steel falchion, glowstone ring and a glow ring, because those are the two rings that I have; Combat skill = 5). Getting a few iridium bars for sprinklers would be
really nice with the greenhouse repair coming pretty soon.

But based on Miretar's comment "Previous visits had me out of those caverns in about 15 seconds with my tail between my legs" I suspect that the 40k to finish the Vault bundles would be better spent around the farm, rather than trying to access the Desert anytime soon.
(I'm on PC, not iOS; not sure what difference that makes).
Everyone has different experiences, and your mileage will vary, but...
I'd say if you just have an extra spicy eel lying around and can enter the cave as soon as the conditions permit for the day, it might be worth a try. On my last farm, I didn't exactly have a fantastic set up for my first few trips (iron pickaxe, steel falchion, level 8 combat, but I did have burglar ring). My very first trip I just downed spicy eel but walked out with four extra bombs, a new spicy eel from an enemy drop, and 39 iridium ore. Got to level 46 or so with the help of a few lucky drop shafts. And with that in mind, I think the burglar ring is also a huge boost. Half the iridium I got wasn't from nodes, but from enemy drops - specifically from cornering big purple slimes, so I could wail on all the little slimes they spawn as soon as they appeared. Burglar ring will also make bomb/spicy eel drops from serpents a lot more likely and make it easier to snowball from day to day, and make each visit feel a bit more worthwhile.
IMO, it is a very good idea to keep a chest just next to the entrance to skull cavern. Then you can store your extra bombs/spicy eel and other things there and not have to remember to pick them up and take them with you. I also strongly recommend keeping omni-geodes on hand. Each trip I usually get 20+ omni-geodes, then drop by the desert merchant to trade 9 for 3 desert totems. It might feel a little steep at first, especially if your museum is lacking, but if you stick with it (and murder those carbon ghosts that drop them often) soon you'll find yourself getting more desert totems than you expend, and you can start cavern trips earlier and progress more easily.
That said, I feel like I've also gotten very good at reading enemy movement and judging exactly when their hitboxes are in range, so even with low combat levels I don't sweat it as much. But if you stick with it I think you'll figure it out better in due time. Just takes some persistence.
EDIT: I should clarify that I always have a nice fat stack of salmonberries/blackberries on me at all times too. Cheese might be more convenient if you like the bigger heal and have the animal/production line for that, but I find upping foraging early on and getting lots of berries during the harvest season works great for me. Might not be in your window of potential right now, but an alternative to keep in mind for the future. If you don't think you can get very deep very fast, though, then killing enemies (especially the slimes - sometimes they just drop whole bars!) until you just get better at that is fine and well too. But if the 40K for the vault seems like a super serious purchase decision and each 500 gold expenditure to visit the desert feels like too much, then you might want to wait off a while to build your production better and work with more stability. Rushing for iridium sprinklers can be tempting, but it's often better to just rearrange the next winter when you can reasonably get them (plus quality sprinklers sell for a decent price when you're done with them anyways, so no shame in making a bunch even if you'll get rid of them later).