Gonna buy my first ETH soon. Couple of beginner questions.

Hello r/ethereum. I have been researching this project for a little while and I am going to buy some Eth soon. I was hoping you all could help me with a couple questions.

1. I am considering either Binance Us (in the usa here), Coinbase Pro or Kraken to buy it as from my research these seem like widely used reliable exchanges with the lowest fees and most coin options? Are these good exchanges? What exchange/trading app is the best to buy Eth on? Why do you prefer it/what are the fees (and are they the lowest/if not why do you prefer it)? Which would you recommend for Eth (or any coin) and why?
2. I want to purchase a Ledger Nano X to store my crypto after buying it. Is there one of these exchanges that is best/easiest to transfer your funds to a hardware wallet like this one? Does anyone here have experience with doing specifically this and could explain or point me to some info explaining how it works?

Thanks in advance!