To search for all available games for a certain console, head up to the top menu on the site and hover over one of the consoles of your choice. Then click "All Available Games" and you will be taken to a list of what's currently available for that console.
Unfortunately, some games will take a while to show up on site. Putting in a request for those games is recommended. Some of the people ahead of the queue, may also be on vacation mode, which means their place in the queue won't count, as they're no longer in the queue for the listing. As well, it accounts for all requests for the game, including the conditions. So it could be 3 requests for disc only.
Requesting disc only gives you more of a chance to match, as you can potentially match for a condition above that condition. But, you risk getting a disc only listing if you're only interested in good or excellent. Each condition has it's own queue in a way. So if you request good, you can match for good or excellent. But, if someone has a request in for a condition above you first, they will pair for that condition first.
It's best to put in a request for every game you're looking to get. Even if there is no listing available.