The initiative roll is based on dexterity and its modifiers. It is rolled before each fight by each participant.
At the beginning of each fight, you launch the initiative by performing a dexterity check. The initiative determines the order of the creature's turns in combat, as described in Chapter 9.
(Basic rules, page 64).
For other controls, the way the campaign is run will depend very much on the type of control used by DM calls.
On page 61 of the ground rules, we find:
Acrobatics, Sleight of Hand, Stealth
Arcana, History, Investigations, Nature, Religion
Animal treatment, intuition, medicine, perception, survival
Deception, Intimidation, Performance, Persuasion
If you are organizing a party full of thieves, you may find that skill and stealth checks are very common. If you have a campaign focused on social interactions, the most common roles are those of persuasion, bullying and deception (charisma). We are in a campaign that has experienced many adventures in nature: the wisdom controls (survival) are very common in both cases and to avoid getting lost, as well as the controls of wisdom (perception) for having noticed the animals / monsters before they notice us.
About "class skills"
Some classes get skill In some skills, but as the skills / abilities check in D & D 5e, everyone can check all the skills (there is a special case for choosing locks, shown here.) You need thieves tools for do not have to be competent with them). My 8 Charisma Barbarian can perform a Charisma (Persuasion) test, although his chances may be lower than those of the Bard. My fighter in the plate mail can do Dexterity (Stealth), although his chances of success may be lower than the Monk's.
Each ability covers a wide range of abilities, including the skills that a character or monster can master. A skill represents a specific aspect of an ability score, and the skill of an individual in a skill demonstrates that the focus is on that aspect. (The starting skills of a character are determined during character creation, and monster skills appear in the monster's stats block.)
Backgrounds also offer skills
The skill is not only determined by the class. a PC Context also has an impact on the skills they possess.
For example, my ranger has a perfect command of Thieve's tools, which he
obtained from his criminal / spy background.
My warlock in my nephew's campaign uses performance as a skill, thanks to Entertainer's experience.
This training offers both acrobatics and performance skills, as well as tool skills in the disguise kit and a musical instrument type. The story of my warlock's cover, when she was not in a dungeon or in the desert, was as a minstrel / singer / troubadour.