Gemini is the fiat exchange I used when I began my journey into buying cryptocurrencies. Fiat exchanges allow you to put in fiat currencies USD and others to buy cryptos. I have had great experiences with this exchange. After creating an account and verifying your information, which took about a day and a half to fully complete, I was immediately able to deposit money and buy btc and eth. Now the downside of this exchange is that those are the only currencies it supports and before you are able to move it they must verify that the money was received which takes about 5 days. Again, I wanna stress you can buy btc and eth during that time, you just cannot move it to a wallet or another exchange so any price movement those cryptos do you take part in. So after I became familiar and comfortable with this exchange and wanted to buy other cryptos I moved on.
I wanted to buy dash, neo, xmr and some others. Now the wallet I use, Exxodus which I love, allows for exchanging a handful of currencies without moving them into an exchange but it didnt have neo or xmr. So I looked around and found bittrex. Moved a small amount of money there and experimented with it. You must move BTC into this exchange to buy other currencies as there is no way to put USD in, so this is not a fiat exchange. Again I had an easy time getting what I wanted and moving it around. Another good experience though it has many more currencies and may look overwhelming to someone knew to the field.
Finally i wanted to buy some iota which wasnt supported by bittrex or gemini. At first I tried to get onto bitfinex but being within the US they wouldnt allow me to use it. So i went to binance. Moved some funds there and got iota. And those funds are still there. I cant move them. I tried to move them but now the funds are suspended and not able to be moved. It also occurred with some xmr i bought on the exchange. So i have a bit of iota and xmr tied up on the binance exchange that i cant move anywhere. Its frustrating. I like to keep assests in a wallet but it is what it is. If they can smooth this process out binance would be alright, but for now im staying away. Now, it may not be the exchanges fault, i dont know who/what is at fault but the currencies may be having issues. However 2 out of 2 that i have purchased on binance are having issues so it leaves a bad taste.
Briefly:
Gemini is a great fiat exchange to get introduced to the crypto field. Its simple and quick but only has 2 currencies.
Bittrex is great once you grow comfortable with a fiat exchange. You can find many other currencies here but will need to move BTC into this exchange to purchase them.
Binance is similar to Bittrex but has other options that Bittrex does not. However, i have had very negative experiences so far.
***as many people suggest make sure you dont move large amounts into new exchanges before getting familiar with them for these reasons. you never know what could happen.