When you talk specific about online wallets then you have few big names like XAPO and Coinbase. There will be always a risk when you store it in an online wallet because they own your private keys. So when you do keep the amounts always low and use for big amounts cold storage so you own your private keys by yourself. Maybe other good option If you use an iPhone then there also exist Bread Wallet(cold storage for mobile).
When you like to gamble stay away from Coinbase they ban people who use there wallet for gambling. XAPO don't ban people so far who use there Bitcoins also for gambling.