With U.S. dollars you can buy over 30 different cryptocurrencies directly! You no longer need to first buy Bitcoin then transfer it to another exchange as an intermediate step. Just change the drop down menu for "PAY WITH" to USD, and you can proceed to invest in alternative cryptocurrencies (or buy Bitcoin itself) directly! Changelly is user-friendly, and a great way to buy altcoins with Euros or U.S. Dollars.
If you want to receive free cryptocurrency by just learning more, try Coinbase. For Europeans, the platform/company Iconomi.com can allow you to buy crypto or learn more.