I wouldn't recommend coinbase. I recently tried to buy bitcoin with them, but they ate my money without processing the transaction. I've sent them an email, so hopefully they are honest and reply to my enquiry, but until then... 
This is not the first complaint I have heard about Coinbase lately but without knowing your exact situation and not using Coinbase myself its hard to help.
Hopefully they will sort it out soon for you.
I cant see them pulling an exit scam but I would still insist that once you do receive your coins take them straight off line to a paper or hardware wallet, or at the very least a wallet that you have full control over i.e. a wallet you and only you have the private keys to.
Yeah definitely. I've been moving my bitcoins to at least a desktop wallet as soon as I purchased them.
I do expect them to eventually end up either returning my money or giving me the purchased bitcoins, but the fact they could accept my money without processing the transaction is a problem in of itself.