If you just want a simple method, a very basic method is to have a list of addresses on your server and a script which hands out each new customer a new address from the list. You can then check the addresses manually, and whenever funds arrive, ship your goods to the customer. How many confirmations you want to have is in this case solely your choice.
A few questions, it looks like bitpay only accepts bitcoin.
How could I generate a wallet address? and how can I verify funds have been sent to that address? Is there a way to do that via linux command line?
Yes of course, by using the original "Satoshi" client (aka bitcoin-qt), which can be found on bitcoin.org. You don't need the "-qt" part with UI, it also comes with a command-line client. You first have to setup the daemon on the server, which can be started with "bitcoind -daemon". When it is running, you can use "bitcoind" to perform various tasks - see "bitcoind help" for a starter.
To generate a wallet address, use "bitcoind getnewaddress" (as the simplest method). To check for incoming transactions, you could periodically run "bitcoind listtransactions" and see if something new happened; also, there are other commands that can be used to extract the balance on addresses.
I do not yet understand what exactly you want to do on your webpage. Is this a shop? Or should it be an online wallet? Something else? Maybe I can help you if I understand that better.