Coinbase is an old and time tested wallet service provider. They are a legal entity. You don't have to buy a whole bitcoin from them, you can buy in smaller fractions as well. However, they have few restrictions which are country specific. So check the faq section before you start the procedure. Also check if you need to submit your kyc documents or not. If you are compliant with their regulations, you are not expected to have any issue with them. I have been using their service since long and have never faced any issue, even though I didn't buy any bitcoin from them. I just use coinbase for storage of my coins.