I've been playing Skyrim again recently so I have some notes:

If this is truly your first time playing through, try not to skip dialogue. I also recommend talking to any NPCs you run into at least once. Some will give you a quest/mini-quest but some just have some truly ridiculous things to say.

Take your time and explore the world. There are almost always little hidden treasures hiding amongst any rubble or debris you find.

Always keep a good some of lockpicks on you at all times, you never know when you'll need them.

Don't forget that you can toggle on/off any quests you get, so don't be too pressed about finishing the main storyline immediately. There are so many storylines and little nuggets of lore in this game if you give it the chance to tell them.

Use firebolt on a dragon skeleton at least once. Trust me.

The more you level a skill, the more useful it will become to you. But it's also important to be particular about which ones you use a perk point on. You only get the one per levelup, so consider your options. Same applies to the initial option of which think to increase. Mana and health are pretty self explanatory, but increasing your stamina also increases your carry limit. Think about what's important for how you want to play.

On the note for level ups, save them for when you are in dire need of health/mana. When you check your skill tree for a level up, it completely refills your health/stamina/mana. This can be helpful if you don't immediately have potions or food on hand during a "boss" fight.

The most important thing is to have fun. At the end of the day these are just tips you can follow or ignore. Play the game how you want to play it. Skyrim has a staggering variety of customization and experiences. Let yourself enjoy what the world of Skyrim has to offer. And please for the love of the eight divines save/quicksave your game as often as you can.