The best and more safety way , to me ( after lot of bad experiences..)
Is using virwox.com
They take enormous fees compared to other exchanges. If you don't mind doing KYC, (heck you're using a Credit card anyways), you should really look for alternatives. Coinbase is extremely userfriendly, but bitstamp et al do the job just fine for 2-4% fee.
As far as I know all those exchanges do not accept credit card payment.
Cex.io and coinmama are the most trusted ones I know that accept credit cards as payment. The fees are higher for credit card, so consider alternative payment methods
I think they might have changed that, (bittrex), but i don't really use them so i might be wrong. https://support.bittrex.com/hc/en-us/articles/360004441491-Fiat-US-Dollar-Trading-Deposits-and-Withdrawals