For variety of coins, Bittrex. You can also open accounts on various smaller exchanges that list specific niche coins.
For comical leverage on the big coins (up to 100x) there's Bitmex. You'll need to sneak in through a VPN if in the US.
For fiat onramps, Coinbase, Gemini, or Bitstamp. Avoid Kraken at all costs, unless you really hate yourself. You have to roll a Natural 20 to have an order succeed there.
I'm not affiliated with them but I like Bittrex. The main thing I like over some other exchanges I've used is the volume. Having good volume for any coin you are trading is important otherwise you end up competing with bots making it very hard to get a fill. Other things I like is very little down time, lots of coins, a decent if not stellar interface, and a good API.
In the cons I wish they would add new coins faster though they seem to be picking up the pace lately. That's about it. All in all, I'm happy with them and would recommend.
to put it briefly, their support left me hanging with a nonfunctional account for 2 months now due to bugs in their site, and have simply stopped responding to tickets.
I would not recommend anyone use a financial service with that level of disregard for their customers.
Bittrex, currently the largest cryto exchange with a lot of altcoin selection. Coinbase, if you're looking to just trade bitcoin, Ethereum and Litecoin
Coinbase seems to piss me off. They have obscure ID / KYC verification requirements that change with the level (monetary value) of your transaction. After I opened my coinbase account I sent them an email asking what specifically I needed to submit have my account fully authorized for an arbitrary value transaction. I resent being requested a different document everyday. They never replied to the email so consequently I never used the account.