Anonymity is a process, not a state of being.
Saying, "I want to be anonymous, if I do XYZ will I be anonymous?"
Is like saying, "I want enough time to elapse, if I wait 3 seconds will enough time have elapsed?"
How anonymous? Anonymous from whom?
Please understand that bitcoin does not in and of itself give you anonymity. Bitcoin is a tool that can be used to increase anonymity when the appropriate steps are taken, but it is extremely difficult to make a payment for a product or service and remain 100% anonymous with bitcoin.
As for your question about how to get bitcoins and use them to make a payment:
Most of the online currency exchanges halted bitcoin withdrawals earlier this week. Some of them may have resumed withdrawals, others have not. A few of the more commonly known exchanges are:
BitStamp
BTC-E
MtGox
You can read about each and make your own decisions about how easy they are to work with and what is required to get payment to them and receive bitcoins from them. As far as I know, none of them accept PayPal, so you would most likely have to contact your bank and arrange a wire transfer to the currency exchange.
If you are located in the U.S. you could also consider purchasing your bitcoins from CoinBase or BitSimple. Each of those services require you to link a bank account to the service. Coinbase requires you to give them permission to take the payment out of your bank account. BitSimple requires you to wire them the payment.
As others have mentioned, you can also search on localbitcoins.com to see if there is anyone near you that is selling bitcoins. In that case you can make arrangements to meet with them and hand them cash for the bitcoins.
Another option is to search through the "Currency Exchange" sub forum on bitcointalk. Many bitcoin sellers there offer bitcoins in exchange for GreenDot MoneyPak or other forms of payment. Be careful to avoid being scammed. Consider using an escrow service provided by one of the more trusted members of this forum:
https://bitcointalk.org/index.php?topic=276897.0