I've got plenty of tips, having beaten it 9 times. Learn to Flurry Rush against tougher enemies (when they swing their sword, backflip if it's a horizontal attack, sidestep if it's a vertical attack). Don't use up your good weapons too fast, I'd recommend reserving the really strong ones for stronger enemies, and use one-handed swords or spears against more agile enemies. Though, there are a LOT of weapons around the game so running out of them isn't a huge danger.
Also you have infinite bombs, and I recommend upgrading them at Hateno Village when you get there. You need Three Ancient Shafts, which you get by killing Guardians, or looting the dead ones. To kill a Guardian, Shield Bash its laser back at it. This might take some practice, but you can always save before facing it and load if you lose too many shields. If you die it'll go back to the last save point.
I would recommend doing the Kakariko and Hateno quests before exploring the bigger open world, but I'd also recommend stopping by any shrines you find along the way. And if something looks out of place - some sort of puzzle, or a rock in a strange place - check it out, you will get a reward.
Always have a torch handy once you first find one, and don't attack enemies with it. And always take an opportunity to pick up some food, and weapons if you have empty weapon slots.
For Spirit Orbs, once you get four, you'll be able to increase your health OR stamina. I'd recommend balacing that out - you'll need 13 hearts to get a specific item later on, while more stamina makes travel easier.