Only refresh Arena attempts if you definitely know the 5 extra attempts will get you into the next reward bracket otherwise it's not worth it. Also the crystal cost for refresh goes up each time, so the first is 50 crystals and the next is 100, I've never refreshed more than once so I don't know if it continues to go up by increments of 50 or if it's double the amount.
If you're just starting out then it depends on whether or not you want to take a chance at unlocking some strong characters using chromium cards. I wouldn't waste crystals just buying 1 card at a time, definitely save up to buy the 8x pack if you can wait.
Otherwise if you're happy with the set of characters you have now and can easily farm their shards and need materials to train skills or level gear then go with an energy refresh. I don't know if energy refresh costs also increase or not right now. I think they did back during soft launch.