More info: learnmeabitcoin.com/technical/keys/private-key/wif/
For public key, hex with compression prefix (pubKey isn't usually required to write in the backup).
More info: learnmeabitcoin.com/technical/keys/public-key/
However, those base64 strings when decoded don't look right,
Better stick to open-source software/hardware wallets than use the output from that script.
But I would only suggest you to send bitcoin from the Exchange to your cold storage wallet when you accumulate a significant amount.
That's not only to minimize the accumulated fee when sending from exchange, but also to minimize the number of UTXO your wallet will be keeping.
The goal is to keep only a few higher value unspent outputs so that your wallet wouldn't have to use a lot of inputs in your future transactions.
The lower number of inputs, the lower the transaction's size will be; lower the transaction size results to lower absolute fee.
If you want to go P2P, you can use P2P exchanges available in your Country or purchase from users in this forum in Currency Exchange board.
Link: http://bitcointalk.org/index.php?board=53.0 (make use the "Trust system" since this is quite risky)