As you said, my coinbase account was banned and blocked because i withdraw few satoshis from gambling sites. I didn't knew that before. That were the newbie days. Now, I would recommend using only desktop wallets instead of some other third party wallets. Another problem with coinbase is that you are not the owner of your addresses' private key !
I would recommend desktop wallets like electrum, etc.
I am using blockchain.info wallet and I am not facing any peculiar problems with them yet. Even I will face any in future, I will simply export and import my private keys into another wallet types and hopefully I will not have any problems with my savings.
If you encounter any problem, like account hacked,etc , even having the private keys would not help as the funds would already had been transferred.