There are so many crypto exchanges today, some offer only crypto trading pairs for example BTC/ETH or BTC/LTC - for instance Binance have almost 250 such pairs so you can easy trade many altcoins for
BTC and vice versa. But if you need to send money ( fiat ) to exchange to buy some cryptocurrency then you need to look for exchanges which offer fiat/crypto pairs, so pay attention to it. Also many exchanges requiring that you need be verified with your documents so that you could use them, and you will recognize it by KCY ( Know Your Customer ) and AML ( Anti-Money Laundering ) just by reading their TOS.
Some of most trusted ( oldest ) exchanges are : Bitstamp, Coinbase, Poloniex, Kraken and some others. Before using any exchange I suggest you to make a review of that exchange by simply use search engine with key words including "exchange+review".