So i'm using coinbase to buy coins.
Question is, should I transfer all the coins I buy out of my Coinbase wallet and into a wallet on my phone or pc?
Isn't that more secure?
Don't want to get Goxed
It depends on what you want to do with it.
If you have it on Coinbase, then you are certainly exposing yourself to third party risk to some extent, no matter how good the procedures they have in place are.
However, I keep a small amount of petty cash on Coinbase in order to be able to spend the coin if I ever run into a random situation where I want to donate coin or I want to buy something. My requirement for being held on Coinbase in my mind is that "If it gets stolen, I don't care that much". If it ever gets more than that, then I move it off the site.
Next, I have what I keep on my PC. There isn't a third party risk, but my computer could still get hacked or my hard drive could crash (so I have paper wallet backups) or other things. I consider this my checking account. I keep a little more than I would have in my petty cash wallet, but if I need the funds it is possible to spend them from my computer or I can send some to Coinbase to refill my petty cash.
Finally, I have paper wallets. Someone needs to have the physical piece of paper in order to get the funds. I keep that piece of paper in a rather safe place (people are much better at understanding what it means for a physical object to be safely stored than they do for a digital object to be safely stored). This is my savings account. I never plan on accessing the funds any time soon, but I will slowly add to the account over time as I make more money. However, if something horrible were to happen and I needed to access the funds or if it was time for me to cash out, then I can import the wallet into Coinbase and sell the bitcoin for cash fairly simply.
Thus, it is not necessarily wrong to put your coin in Coinbase. There is a question of how much risk you are willing to take, which always has diminishing returns and never is 0% risk. There are the questions of how much you might spend, how much you are willing to lose, and how much of the coin you need access to at a moments notice vs how much you can store and not really try to spend it for the next several years.
Try to pick a method or a funds distribution that best answers these questions for you, and understand that no matter how well a company is run, if you keep money with them then you need to trust them to that level in order to let them hold your money.
I think Coinbase is run much better than Gox, which is why I use them. However, there is no need to expose myself needlessly to the risk that they might fail.
Hopefully I was helpful in my description and didn't make things too complicated for you. I would be happy to explain something further if you would like.