What are you heading into Skull Cavern for? There are some great goodies in there but the strategy may be different depending on what you want. And focusing on ONE THING per run may help to keep you focused on success. In general, these are always good:
High Luck day
Staircases
Galaxy Sword (or the Lava Katana if you don't have the Prismatic Shard
@Yvi mentioned yet)
Good healing food (I use
Cheese but Salads and others are also good)
Space Boots or better
Slime Charmer Ring (very useful for ignoring slimes & staying focused on other things)
and always your Pickaxe and if you prefer, a way home (Farm Totem, Return Scepter). It's also OK just to pass out there at 2am and pay the 1000g.
My strategies for certain items.
Auto Petter/other Treasures:
Take
Lucky Lunch for that big Luck Buff and
Coffee for speed if needed. Just slap down Staircases because all you're looking for is Treasure Rooms. Rarely you will be trapped by rocks where you can't put down Staircases, so have your Pickaxe ready to clear a spot.
Iridium/Gems/Radioactive Ore:
Take
Bombs and
Lucky Lunch/Coffee or
Spicy Eel/Ginger Ale as you'll be fighting more monsters and maybe getting Spicy Eel drops from Flying Serpents. In reality I plan to Staircase down to Level ~100 and then start evaluating. Lotsa monsters (especially Serpents)? Staircase down one more Level and have another look. Calmer with some decent ore concentrations? Bombs awayyyy! Always keep an eye on your Health. If you even get close to half Health, eat a Cheez/Salad/etc. Your Health is most important, full stop.
Monster Hunter goals:
Take
Spicy Eel and
Coffee for Speed and a little Luck. Staircase down to Levels with your favorite monster that are fairly clear of stone/ores (or a Prehistoric Floor) and take care to position yourself with everyone only on one side of you as you can outrun everyone. Then hack, slash, and EAT FOOD to heal.