I'm not usually the type to say there are right or wrong ways to play a game, but BoTW definitely is a game whose enjoyment is built around the player making their own pace and exploring however they want. It's a VERY different game from the previous Zelda's so going in with a fresh perspective and no expectations carried from past games might help you get into the game quicker.

So for now, I would suggest that you don't worry too much about weapons; you'll always find something you can use when/if you need it.

I also highly recommend turning off objective markers if you truly want to feel like you're exploring the world. The game's NPCs are pretty good at giving directions especially since they reference areas by name and the map's areas are always labeled. Forks in the road and pathways are usually marked with signs, and beacons, stamps, and the Hero's Path mode makes sure you always know where you've been and where you might wanna go.

The most fun I've had was always been getting distracted on my way somewhere and getting rewarded for my curiosity. (either with more weapons, korok seeds, or even shrines)
---
"Splashing water on a pervert is like putting lasers on a shark" - Shiho Shishido

Got Zelda: Breath of the Wild for Christmas

[none]

[none]

---