There are hundreds of cryptocurrency exchanges available to users nowadays. Since the huge rally of the crypto market in 2017, lots of companies are cropping up offering a new exchange.
What you need to know is that there are essentially four types of cryptocurrency exchange.
These are the exchanges that allow you to buy a cryptocurrency directly using your fiat currency (a government based currency such as the US dollar or the British Pound). These are most popular with those who aren't familiar with the crypto market because it allows for easy access to the cryptocurrency of their choice without much hassle.
The issue with these exchanges is that they don't seem to offer a choice of coins, so if all you want is bitcoin then they're great but for a more peculiar altcoin.
These exchanges will only allow you to buy one cryptocurrency using another. This means that you will need to buy a cryptocurrency on a fiat - crypto exchange and then send it to the wallet of the crypto - cryptp exchange before exchanging for the coin you want to buy in the first place.
This is normally for more experienced traders who are actively trading between coins to profit quickly or alternatively want to buy smaller less known coins.
Peer-to-peer exchanges are those that simply match a buyer with a seller and will not take the other side of a trade. The most famour example is Localbitcoins, who will match a buyer with a number of sellers (if they're available), which then gives the buyer the option to choose the best price of the selection.
They will normally offer an escrow service so that there is reduced counterparty risk for both buyer and seller.
Brokerages are not strictly exchanges because they do not allow you to own the underlying cryptocurrency. However this does have it's pluses because you don't have to go through the hassle of setting up a wallet.
What they offer is a CFD product, which allows you to speculate on the price of bitcoin and other cryptocurrencies without being exposed to the same risks that exchanges offer. The main risk being that they are unregulated, whilst brokers must follow a strict set of rules laid out by the regulatory body they have a license with.