Personally i am using Coinbase as it is not restricted in my country.
As a second alternative I would suggest Kraken as they have low fees and you can buy/sell Bitcoin or other cryptocurrencies easily.
For your second question, yes you can store your crypto on the Nano S as long as you bought them.
Coinbase I absolutely do not like, for many reasons. So I would still recommend Kraken
Can you please provide us your reason why you think it is not good or you don't like to make use of coinbase as a means of buying and selling your crypto currency and why you recommend Kraken.