You NEED a better sword for Skull Caverns, full stop. You probably have the Obsidian Edge you got from a chest in the lower Mine levels but the Lava Katana is your best bet until you spend your first Prismatic Shard getting the Galaxy Sword. More damage makes all the difference to make the Caverns manageable.
Food is opinion but IMO the best mostly passive food is Cheese because with an AutoGrabber you get the Milk with no effort and all you need to do is put that in a CheezMaker and you have your food. If you need a lot of food immediately and can pay, a lot of people like Salads you can buy in bulk from Gus.
Rings are also a lot of opinion. For me the best rings for peace of mind in SC are:
Slime Charmer - just ignore slimes, they're effectively not even there
Iridium Band - mix of good QOL effects
Later on when you can knock Rings together, mixing those with Lucky Ring and other different ones can make fun combinations. One thing not to overlook is Luck when going to Skull Caverns. Go on Lucky Days and take any Luck Buffs you have, like Spicy Eel and later on, Ginger Ale. These get you increased Ore spawns and most importantly:
Treasure Rooms!
You gotta have some fun in there!