I bought it on Coinbase because it seemed convenient; not sure if that was a good idea or not. Is it safe to just leave it on Coinbase?
Cryptocurrency exchanges are like banks, if banks had no fiduciary responsibility, were started by trust fund kids that sort-of know how to code, off-shored all their hard work to people they've never met, hired no security and came up with their own arbitrary ideas as to how to make "locks."
No, it's not safe. Go to myetherwallet, generate a wallet, print it out on paper, copy-paste the address, and send that money directly out of coinbase and to your wallet. If you want to make sure it works, send like .01ETH or whatever to make sure you understand the process.
Here is a list of targets. Now imagine several tens of thousands of bored hackers and social engineers. When your money is in an exchange, your money is on that list.