first some terminology that i find "not-so-right".
you are using a web wallet not online wallet. and it is called blockchain.info not blockchain

to answer your question it is best if you use a "software" aka desktop wallet because web wallets have lots of risks.
read:
https://bitcoin.org/en/choose-your-wallet
https://bitcointalk.org/index.php?topic=1631151.0

and to be even safer you need to learn more about cold storage.
https://en.bitcoin.it/wiki/Cold_storage
http://docs.electrum.org/en/latest/coldstorage.html

and to buy bitcoin if blockchain.info doesn't accept your credit card you need to try and see which bitcoin exchange service accepts it (not sure which one works with Greece banks) check kraken, bitfinex, bitstamp, cex.io, btc-e.com
or check out localbitcoins.com