The way to buy bitcoin that is most inline with the philosophy of cryptocurrencies is of course to avoid third parties. At LocalBitcoins.com you can by directly from peers located near you.
Coinbase is the world's largest crypto company and provides both a wallet and simple ways of buying and selling bitcoin. Also, you can earn crypto simply by learning through their program Earn.
Kraken has been serving Bitcoin traders since 2011 and is one of the most popular exchanges around. Create an account and deposit using a bank transfer (SEPA within Europe).