First Bitcoin transaction When making your first bitcoin transaction, at what time do you generate the public and private keys and how do you store your private key on a hardware wallet?
at what time do you generate the public and private keys


Your wallet (the software managing your keys and your connection to the Bitcoin network) handles this for you, typically just before you generate an address to receive a payment.


  how do you store your private key on a hardware wallet


The hardware wallet comes with a software which handles the storage of the key(s) on the hardware.

You might want to take a look to the wiki page about "storing bitcoins" and follow the links :).