Accepting Payments To Bitcoins
I don't know of any service that handles all of these. You can use Coinbase to accept bitcoin.  If your Paypal account deposits the fiat to a U.S. bank account, you can also use Coinbase to manually "buy" Bitcoin into the same Coinbase account.

If you knew the value of your USD account, you could automate the buying of bitcoin via Coinbase API.  Manually doing the conversion every week, month, etc would not be a bad idea though because you could wait until the Bitcoin price is low, or just keep a part of the funds in fiat for your business expenses.

If you are outside the U.S., probably better to look into Bitpay.