Monero is the coin the board recommends when privacy is any part of why you are here. It hides the sender, the receiver and the amount by design, so the payment is not legible on a public ledger the way Bitcoin is.
A wallet you control
Use Feather on the desktop or Cake on mobile. Both keep your keys in your hands. Cake also carries a built-in swap that converts Bitcoin to Monero without an exchange in the middle, which is the common way people move an existing Bitcoin balance into Monero.
The deposit
Open the order, copy the Monero deposit address Awazon issues, send from your wallet, and wait for the confirmations the market asks for. Monero confirmations are quick and the network fee is a fraction of a cent.
Acquiring it without KYC
Peer-to-peer options and in-wallet swaps let you get Monero without an identity-checked exchange. See non-KYC funding for the routes.