You can buy Bitcoin using your Credit card or debit card and bank account from many websites. We have given some video tutorials If you are unsure of where to buy bitcoin or how to buy bitcoin by credit card and bank accounts.
Coinbase is an USA based company. you can buy bitcoin and other many crypto currencies from this website using both your us bank account and bank cards.
Here are some more of the popular & legit Bitcoin websites where you can use your debit or credit card to buy bitcoins. I have tested these all myself.
Regarding using a credit card, most of these sites use your cash limit on the credit card, so you need to check with your bank to find the limit of your credit card.
More site list