Buying bitcoins with credit card or Paypal is possible, but usually very expensive because the seller has to cover for the risk of chargeback. Bitcoin transactions are not reversible, so if you dispute the charge the seller is in a very weak position.
Cex.io is an exchange that offers credit card purchases to its clients, but you have to go through several id verification process that will probably make you uncomfortable. After buying you would just need to make a withdrawal to the desired Bitcoin address.
If you are open to using your bank account instead of a credit card, you have more options, but which are available to you will depend on where you are. A couple well known ones are:
- Litebit.eu. They accept SEPA bank transfers and a few other lesser known payment methods (iDeal, GiroPay and a few others). You just make the payment and give them the address.
- Coinbase.com. They are one the biggest exchanges out there and many people use them as a wallet (they are not wallet because they keep custody, not you, but that is another discussion). You can link their account to your back account and make Bitcoin purchases. You then can send your bitcoins to whoever you want. However, they have closed customer accounts in the past if they detect that you send funds to services they don't consider legal, like gambling sites, so if that is your intention I would not use them.
There are many more if you make a couple Google searches, but I have mentioned only services that I know have worked well for people I trust.