The image below shows one possible progression of your nature deck as you play for free. Everyone starts with the "Welcome" set of cards. As you play, you will unlock more cards for free from the "Core" set.
You won't be using this exact deck for long because core cards are gained quickly. Even so, this deck provides a smooth mana curve to keep you in the game through 6 mana. You'll also have lots of options for the early game with 15 cards at 2 mana or less.
As you open core packs, be on the lookout for the following common cards:
This is where Nature starts to develop its unique identity: big creatures. Nature creatures have some of the best strength and hitpoints per mana spent. To compensate, many creatures are confused. Learning to play well with this randomness will separate good nature players from bad ones. It takes practice.
Charging Oryx is added in at 7 mana as you now have the tools to last that long.
Each "Core" rare pack you open has 4 commons and 1 rare card. As you slowly build up your rare collection, be on the lookout for:
One of the best early combos for nature is Marsh Walker + Shieldbearer. Shieldbearer has been nerfed slightly recently (from 1 strength to 0); however, having a 2/5 Marsh Walker with regen will win you games in the early ranks. Try to line this combo up during the mulligan phase. Lightning Strike is a great reaction card and should be saved for when your opponent drops big creatures (preferably alone on the board).
All rare packs have a small chance to give epic cards, and every 10 levels you earn an epic pack that has a guaranteed rare. (You earn legendary core packs every 25 levels.) These will take time, but be on the lookout for:
With the inclusion of Wildfire, the deck strategy changes. Now, you'll want to get many wild creatures on the board and hit them with Wildfire. Valewarden Minotaur is a great card. 5/5 stats (without confused), provides healing, and gives you a card if you are at full health. Finally, Faeflame Blade is an absolute beast for controlling the board early game. As you get the feel for it, you decide to run two of them.