There are several factors that one has to consider when choosing a Cyptocurrency Exchange, below are  9 such factors:

1. Protocol 

Is the exchange based on a Decentralised or Centralised Protocol. On the difference between these two read the article titled

2. Fees 

Each exchange has it own deposit  and withdrawal fees some are low for certain currencies and high for others giving a opportunity for arbitrage.

Fun Fact: Sending funds to someone who uses the same exchange attracts no fee all on some if not all exchanges.

3. Cryptocurrencies supported

The more the cryptocurrencies supported the better. DEX protocol normally focuses on tokens associated with the blockchain they are built on top of.

4. Deposit and Withdrawal options

An exchange that provides several deposit and withdrawal options is a good one. 

5. Geographical coverage

Some exchanges do not work in certain countries so check and see whether the exchange you are choosing serves your current geographical location this rule normally applies to centralised exchanges

6. Verification 

Some exchanges make it mandatory for individuals to complete KYC by sending ID documentation, residential address, phone verification, as well as a selfie of the user before they can perform transactions.

7. Exchange rate 

Exchanging one cryptocurrency for another is cheaper on one exchange and expensive on another so consider such things as you choose an exchange.

8. Reputation 

The rank and user reviews of  an exchange is are important factors to also consider when choosing an exchange. These can be found on the internet and cryptocurrency communities like bitcointalk

9 Security procedure

A safe exchange must have 2FA as a security option. 

10. Liquidity

An exchange with high trading volume and liquidity is a great place to trade