Bitstamp is one of the most popular fiat to Bitcoin exchanges. It was one of the first big exchanges and it provides customers with a platform that is secure and easy to use. It was originally started in Slovenia but has moved its' operations to Luxembourg.
Bitstamp uses MultiSignature technology for its hot-wallet, as well as a fully insured cold-storage option where kept off-line. They also offer a number of other security features such as two-factor authentication and confirmation emails to enhance account security.
Bitstamp provides the option for limit orders, stop loss, and trailing stop orders. They have an easy to use API that can be integrated into user applications. T
Overall, Bitstamp is a secure and reliable exchange with good liquidity and a solid infrastructure. It is a good option for beginning traders as well as more advanced crypto holders.
Trading Fees: Tiered system depending on volume ranging from 0.1%-025%

Bittrex is one of the largest crypto to crypto exchanges. It offers a large number of trading pairs, but do not allow fiat to crypto trading. Bittrex has one of the largest trading volumes in the market.
It is a reputable exchange with good record on security and is also fully regulated. They provide two factor authentication as well as a number of other options to secure funds. They are United States based and are fully compliant with all laws.
They support more than 190 cryptocurrencies and have a dynamic platform. It’s a good option for both advanced and beginner traders; providing advanced tools like candlestick charts and crosshairs, but with a user-friendly interface that is very intuitive.
Trading Fees: 0.25%

BigONE is an exchange that is backed by the blockchain investment firm INBlockchain; an influential investment company that has also invested in EOS, ZCash, Steemit, and other blockchain projects. Several of the companies in INBlockchain's portfolio, that have tokens, are traded on BigOne. BigONE's influential investors give the exchange a high degree of financial stability. The platform is known for its interactive crypto charts and trading tools.

Trading Fee: 0.1%
Withdrawal Fee: 0.002 BTC
Number of Tokens/Coins: 76

BigONE has its own token (BIG) that gives holders a discount on trading fees