Coinbase and Localbitcoins are best choice for the people who want to invest and buy the coins. I am not sure without crypto coins you cannot go to bitrex to buy it moreover they would not allow people to sign up all the time.
If you are Europe you can go to Coinbase to buy, Asian countries not more supportive to buy bro. Once after you bought the coins do not keep that fund on trading site itself. Keep it safe on Segwit wallet like electrum for your safety.
I would definitely go for Localbitcoins (LBC) over any centralised exchange. For a newcomer, I think you should really experience your first buy from a peer-to-peer platform like LBC.
1. Price-wise, they're pretty decent, depending on location. Don't let the trades there fool you, they might seem expensive but what you buy is what you get (all the fees are already included in price), unlike the rates published at others like Coinbase, where you'll receive a smaller amount after fees, commissions, exchange rate. So for a newbie, I think it's best if you want 1 BTC, you see instantly the price you have to pay and you get exactly the amount you bought.
2. Speed. We've all heard about problems with exchanges. Delays in verification, poor customer support. With LBC, depending on your mode of payment, you get your Bitcoins quickly. All my trades in my home country are with online bank transfer, which can even be instant, so I conclude them in less than 5 minutes.
3. Safety. Choose only LBC's online trade so you're protected by system escrow. Meaning, when you confirm the buy trade, the BTC is locked in escrow pending your payment. It's one of the most secure ways to buy Bitcoin I know of.
Either way, whichever place you eventually choose, my advice is always to fully verify your account first before attempting to trade. You don't want issues AFTER you've bought.