DnD 5e - Adventuring Gear
"Adventuring Gear" covers a broad range of items commonly purchased by adventurers. I'll cover some important items below, but I strongly recommend reading the full text of all of the items in the Player's Handbook. Item descriptions start on page 148 of the Player's handbook and run through page 153. The Adventuring Equipment table is on page 150.
Page 151 of the Player's Handbook includes the "Equipment Packs" sidebar. Equipment packs are included in the starting gear options for each class, but if you're using the "a la carte" method where you start with gold rather than pre-selected starting gear from your class and background, you can buy equipment packs using your starting gold. The sidebar says that some of the packs may be cheaper than buying their parts separately, but I haven't checked.
This section discusses a few important items which may not seem immediately important for new players.
Chalk works on most surfaces, making it a great way to track places you've explored in dungeons, to mark items for sorting and the like, and to illustrate plans to the party when an ink pen wouldn't be convenient. It's dirt cheap and so light that it doesn't list weight, so there's little reason why you shouldn't have a few pieces of chalk among any adventuring party.
At just 5gp for a 10-use kit, the healer's kit is a crucial option for any party member not capable of magical healing. It has a single function: you can use an Action to stabilize a dying a creature. If the only person in your party who can cast healing spells falls to 0 hit points, the nearest person with a healer's kit should run to their aid to stabilize them before anything horrible happens.
You can also stabilize creatures using a Wisdom (medicine) check, but that's the only important function of the Medicine skill, so why would you every get proficiency in Medicine when a healer's kit costs just 5gp?
Sure, looking pretty in a dungeon is great, but that's not why you're getting this. Peering safely around corners can save your life. Even a quick glance with a mirror can save you from something literally eating your face when you poke your head around a corner.
Important for lighting lanterns, but also usable as an improvised invendiary device. The official text specifies how it functions if you pour it on a creature then burn it, as well as how it behaves if you dump it on the floor and burn it.
A crucial dungeoneering tool, a 10-foot pole is exactly what it sounds like: a 10-foot long wooden stick. Its sole purpose is to poke things while keeping its owner reasonably far away from things which might be hazardous to their health. Clever adventurers exploring dungeons remember to touch most things (including floors, doors, chest, etc.) with a 10-foot pole before risking their fingers.
Potions of Healing
This one's a bit more obvious than the other item's I've mentioned, but potions of healing are easily overlooked. At 50gp they're expensive at low levels, but they restore 2d4+2 hit points, which is more than some characters get from a hit die (mostly sorcerers and wizards). You can also use it on allies who are at 0 hit points to get them back into a fight.
I've gotten numerous parties out of tough spots by convincing the party's healer to wear potions of healing in a bandolier on their chest, then sending a party member to retrieve a potion and use it on the healer when they dropped to 0. It's obviously more expensive than a healer's kit, but it has the added benefit of allowing the recipient to continue fighting.
If you've read Lord of the Rings, you understand why rope is important. If you haven't read Lord of the Rings, consider how important it is for real-world camping, or real-world rock climbing, or real-world survival scenarioes. My point is that rope is really useful and you should buy some.
Other Stuff You Can Buy
The Player's Handbook presents some other things to spend your gold on: Food, Drink, and Lodging for when you're traveling and just want to buy a hot meal and not sleep in a tent; Services for when you need something mundane like sending a letter or hiring a coach; and Spellcasting Services for when you need someone to cast a spell that no one in your party can cast, like Raise Dead when you don't have a cleric. All of these options are detailed on pages 158 and 159 of the Player's Handbook.