Buying it using credit card is not a good idea. There is even the possibility of hidden fees on some websites.
I think if you are patient and buy using fiat, you will have a better return on your investment.
Buying with credit card is not a good option as you also need to disclose your identity and give all your personal information, for me the best way is to buy in cash on localbitcoins where I simply deposit cash into traders bank account and upon receipt he transfer bitcoins to my bitcoin wallet address.
No problem with that if you really need bitcoin, you can disclose your identity if you are not doing anything illegal. Besides bitcoin is just a currency and it's not illegal to use it, you have to get your goal regardless of your purpose why you are buying bitcoin.
yes that is not necessary to become hidden while purchasing bitcoin or using it, it is a fact that if you are not involve in some illegals activities there no need to worry if your name or identity is disclose to some one,