The website I am using is asking for a "Payout Address" where the centralised escrow is released to the seller, and where buyers refunds are sent.
I don't know anything about the website you are using, since you haven't told us which website it is.
However, if they are asking for a "payout address", I'm guessing that this is the address that they will use to "payout" bitcoins to you when you sell something, and/or the address that they will use to "payout" refunds to you if an item that you purchase is not delivered, or if the item that you receive does not match the description on the site.
Therefore, it sounds like they probably want you to provide them with one of your "receiving" addresses which they will use to send bitcoins to you. That sure sounds like someone paying you.
As for how you add bitcoins, first you'll need to get some bitcoins from somewhere. You can use a bitcoin exchange (such as Coinbase, Circle, BitStamp, Bitfinex, BTC-e, etc), or you can find someone locally that is willing to meet up with you to exchange bitcoins for cash (services such as localbitcoins.com can help you find someone), or you can provide products or services to others and accept bitcoin as payment, or you can use a service such as BitWage to receive a portion of your salary in bitcoin.
Wherever you are getting the bitcoins from, you'll give the bitcoin provider a receiving address from your Bitcoin Core wallet, and they will send the bitcoins directly to your wallet. Once you have some bitcoins, you can use the "Send" tab to create a transaction to send some (or all) of those bitcoins elsewhere. The website that you are using should provide 1 or more bitcoin addresses to send to when you want to send a payment to them.