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Look at Coinbase.

Yes I've had good trading with Coinbase.

Thanks Gregory M.

or bitstamp.net if you are in Europe. Next day SEPA transfers without a fee.

Also worth noting gdax which is part of coinbase but is a trading platform(harder to use) charges much lower buying fees. You can transfer coins/money between gdax and coinbase without fees using the same login/account.

Thank a lot @tonyh will look into it.