Here in US, coinbase is the best source as they are insured against hacks / thefts / loss. Use two-factor authentication on any exchange you decide to use. There are several others in US - Kraken, Poloniex, Bittrex etc.
But in terms of best practice, your crypto wealth is best stored offline on a paper wallet (if you are the responsible type, putit in a ziploc bag / safe box), or store your private keys on a hardware wallet (like Trezor). Hope that helps for a start!
Hi Thomas, if you want to have a better understand of Bitcoin and the Blockchain technology my advice is to join the following course, https://digitalcurrency.unic.ac.cy/free-introductory-mooc/. This is for free and will provide you with a useful overview on Bitcoin.