I use BlockChain.info wallet since end of 2015 and never had any issues. Now I'm not very active there as I changed my strategy, but the wallet is still there and safe. There are several security mechanisms you can set to make it stronger, but as we are talking about an online wallet the risk always exist and people always fear trusting their money to others.

If you don't have much money I think there isn't problem to use that wallet (or Coinbase if you prefer), but once you start having more Bitcoins you will need to split this amount among several sites or you will need to put the BTCs on a safe desktop wallet. But between the two online wallets I prefer BlockChain.info (more decentralized service).