Do I draw cards or reveal Battlefueled first?

According to the standard Start of Game procedure, you determine your Battlefields before you draw your opening hand.

The sequence is as follows:

1. Reveal Legends
2. Choose Champions
3. Determine Battlefields
4. Decide Play Order
5. Resolve Mulligans (which involves drawing your opening hand of 4 cards)
6. Start the Game

As noted in the RiftJudge FAQs (specifically FAQ #7149 and #3373), battlefields are revealed and selected before determining turn order and resolving mulligans. You draw your opening hand of 4 cards as part of the setup process (Rule 116), which occurs after the battlefields have been established.