Question about exchange to wallet moves

So I was hoping to get into crypto so I thought I’d buy some bitcoin just to hold onto it for long term , I than tried moving to a hot wallet named blue wallet. While I wait for my cold/hardware wallet to get here , but realized I’m paying the transfer fee for btc to go to my hot wallet in bitcoin it seems? How would I go about reporting this or can I wait till I sell eventually to report it? i thought I could just buy and move and not worry about taxes until I sell?

Sorry but I’m a legit beginner to this but have been doing my own research a few months before actually buying.