I personally started with Coinbase. It’s easy, you can buy directly by credit card or bank account (BTC, ETH or LTC) and it’s safe (90% is stored offline and hot wallet is insured).
Here is a referral link that will credit both accounts with $10 to start investing: https://www.coinbase.com/join/592b392bb42f8d02a48e7520
Once you start investing more, you can transfert your coins from Coinbase to a cold wallet (offline) to store it long term. I use Jaxx, which also allows you to exchange your coins between 6 different altcoins. I also transfert a portion to exchanges like Poloniex to diversify and invest BTC into other altcoins.
I am currently holding on ETH (50%), BTC (30%) and the rest on SC, GNT, XEM, XRT
I am curious to hear how others have started and are doing today. What is your portfolio strategy? Any favorite 
I use Coinbase too. I really like the user interface and the ability to create multiple Bitcoin, Ethereum, and Litcoin address. And you can easily transfer between accounts for FREE!
I also have had success with Genesis Mining. I started an Ethereum contact before the price explosion and it has paid off well.
I am currently at 66% Ethereum, and the rest in BTC, LTC, GNT, DASH, and DOGE (stored in a offline wallet).