Bistamp is one of the most reliable Bitcoin exchanges nowadays. They are very well-connected in the industry. The company has attracted significant investment from Pantera Capital, one of the biggest Bitcoin-specific venture capital investors, owned partly by Benchmark, Ribbit Capital, and Fortress Investment Group. They also work with Coinbase and other popular exchanges.
In terms of security – it offers two-factor authentication and a password, which needs to be changed every 90 days.
Bitstamp stores 98 percent of all coins in cold wallets, keeping the customer’s funds offline in secure vaults. The remaining 2 percent are held for a live trading on the exchange.
The interesting fact is that the Bitstamp was the first major trading platform to incorporate the best security practices in the industry such as a fully insured cold-storage, two-factor authentication, and mandatory confirmation emails in order to increase the security of the users.
Also, I personally use it for trading and I never had even the slightest problem with them, so Bitstamp is definitely a safe way to buy/sell and store Bitcoins.