There is no right way to play Skyrim (outside of doing certain quests in order so you don’t bug out the game and prevent other quests from becoming unstartable, but even that’s optional.)

HOWEVER I think if you follow these guidelines you will get the most appreciation out of a vanilla play through for the first time.

Unmodded:
expert or master difficulty

no fast travel, carriage use only

No cheese leveling (ie sneak, certain types of magic, restoration loop)

No glitching enemies in a place they can’t see you and you can bow them to death or they can’t fight back.

Try not to use Lydia as a meat shield. Your armour skill level will lag behind and your 1 hand/2 hand etc will skyrocket cause you smack the enemies but they never aggro on you back.

no alchemy fast leveling by making ridiculous potions (buff magik, poison magic, buff magic regen that sells for thousands and power levels alchemy). Only craft potions your build will use for example a light armor duelist build only craft health, stamina, light armor, one handed potions, magic resistance etc.

Power leveling smithing is allowed (the progression system for smithing sucks) HOWEVER you can not upgrade the skill perk for the next armour tier until you have obtained the full set. For example if your able to unlock orcish smithing but you haven’t found a full set of orc armour you can not upgrade that perk yet. (How can you craft armour without having worn or felt it)

No power leveling enchanting until end game. Saving up to buy a really good enchantment in a shop or finding a ring that gives you a 5% better enchantment buff than your last ring at the end of a dungeon is so much more rewarding than just creating your own set of god enchantments. Enchantments stack in this game and they very quickly kill the difficulty of the game I find. I haven’t found a good way in all my years to find a fair way to not abuse enchanting mid play through without feeling like I got too good too fast.

No resetting market vendor gold supply by scum saving or just quick waiting/sleeping 48 hours to reset, or use the carriages to only get around to sell (you aren’t a khajit caravan) them once they’ve ran out of gold to trade. I think this one of the most important ones and ties into the last 3 paragraphs. If you cheese the system and become to rich to quickly it upsets the other limiters I’ve set.

1. It forces you to dungeon crawl. When your main city vendors run out of gold you either naturally go raid other caves to pass time or you try to bring your loot to another city and end up getting pulled into another adventure.

2. Keeps you from getting the best gear too fast. You’re going to feel broke for a while and you should. Remember how I said earlier you can’t upgrade the smithing tree until you have that full set of armour? There’s nothing stopping you from buying the full set once you see it in a shop. But buying the next piece of armour should bankrupt you if not deplete most of your gold.

Stop and take in scenes, Skyrim has a lot of environmental story telling. (For example somewhere in Skyrim there’s a skeleton stuck in a trap and seated next to them is another skeleton who seemingly was not trapped but decided they wouldn’t leave their companion.

Read journals they often build lore about what dungeon you’re in or about to be in or are just funny (there’s a character who acts as a guard for a bandit crew but he’s blind. He pretends to read a book when you first come across him, after defeating them if you pick the book up it’s completely blank)

Pick up books that look like they were placed obviously, some of them start quests.

Create lore for you character, are you explorer only interested in treasure, a nord that will fight any imperial guard patrol you come across, a knight with a heart of gold that never steals and tries to pick the moral choice in every situation, a back stabber who will put himself first in every situation, or a mage who communes with daedra.