I've only been trading in small BTC amounts though so not sure if you'd hit liquidity problems if trying to trade large amounts (kraken's volume is quite a lot smaller than the bigger established players like bitstamp)
Bitstamp is also good, I hear, but I just went with finex because their fees are lower =P.
I think it is important to use an exchange outside the US though, because I expect the fed to start going Orwell on any bitcoin company soon.
There's also the Canadian https://www.vaultofsatoshi.com/, which seems to be top notch as far as the tech (multiple 2FA options, OpenPGP cryptography for email, etc.).
Removing the limit involves buying coin from them, waiting 30 days, and solving some seemingly impossible credit report based identity quiz (some people report passing after 10 tries, you're limited to one try per 24 hours).