gubyy,
Welcome to the forum and the world created from Bitcoin. First thing to know, you're going to find a ton of different opinions here. From "yes" to "no" to everything in between...for every question you ask. Take each opinion in do some of your own thinking to make the best decision possible.
What percentage is this $1200 of your total savings? if it's 10% or greater you should consider offline storage. The risk is low that you'll lose your coins from Coinbase or the other major exchanges, but it has happened once in the past to a major exchange and therefore everyone is skittish.
You'll hear the phrase "if you don't own your private keys, you don't own bitcoin." This is true. But it's no different than the cash you leave in your local bank.
The reality is that if someone steals your coins it's nearly impossible to get them back and this is why most people use offline storage for the bulk of their savings. So you need to think about what amount of money are you willing to lose. If this $1200 is all of your savings, protect it as best you can.
Here's a list of several different wallets based on what you're looking for:
https://bitcoin.org/en/choose-your-walletGood luck to you!
A hardware wallet like the Trezor or Ledger would be the ideal solution. Those allow you to store a number of altcoins as well and would be the safest method for storing your coins especially if you aren't actively trading them.
You are probably fine leaving them on exchanges as long as you trust the exchange, but if anything were to happen to the exchange, you might not be able to recover your coins. ( Mt Gox for example ).
Great thanks for your input, these are all things I will consider. Glad to be a part of the community