Hi and welcome to the board.
A rescue dog is a wonderful choice but isn't right for everyone. I'd suggest reading this good article, which suggests some questions to ask the shelter:
http://www.padsonline.org/index2.php?option=com_content&task=view&id=12&pop=1&page=0&Itemid=4
I also have a lot of links for further reading pinned to the breed rescue section.
Most likely these puppies are unwanted puppies from a puppy mill being offered through a rescue (many legit rescues get puppies in this way). These have papers though -- which is a little odd -- I'd be wondering why a rescue would sell on rescue cavaliers WITH papers as that makes them prime targets for disreputable breeders. I'd ask the rescue why they are giving them out with papers, and highlighting this. The reason why, is some 'rescues' are actually fronts for actual puppy mills to sell on surplus puppies or problem puppies. Few legit rescues would be offering unneutered rescue dogs with papers to avoid any possible risk of a new owner trying to breed for profit (saying they must be neutered later isn't usually adequate for a rescue if they are also giving out the papers). So I'd want to sound out this rescue a bit to understand how and why they are offering puppies in this way and make sure I was satisfied with the answer.
Regarding the pups themselves: I'd want to know why they are available and I'd want an honest answer as they seem fairly young to be unsold from a pet shop for example -- such puppies sometimes come into rescue but usually are much older.
The other consideration on a rescue of any sort is, you don't now the health background of the puppies. These almost certainly will not be from a breeder who has ever done so much as a single health test on the breeding dogs, putting them at higher risk of health problems, and there are some serious health issues to learn about in the breed: MVD and SM in particular.
That said: any puppy can have problems, most cavaliers will eventually get MVD, and the fact that a puppy or rescue dog comes from an unknown background and might be at higher risk doesn't make them any less adorable and deseving of a good home. It's just that not everyone feels ready for those uncertainties and people should be honest in weighing up what they feel ready for. If buying a puppy through a breeder it is very important to research breeders meticulously. The plus of a good breeder is they will know their breeding dogs and lines well, will choose for the best health and appearance, and will always be there to offer full support and will always take back a dog (as will a good rescue of course!).
I run Irish Cavalier Rescue and have a rescue cavalier myself amongst my crew of three.
I do always go thru the health issues with new owners and prospective owners so they know what to watch for; but I'd never want the health issues to dominate anyone's concerns. Just as with people, any dog can unexpectedly get sick. But I do want prospective owners to understand that rescues are always a bit more of an unknown because their background is unavailable to the rescue, most of the time.
If you opt for a rescue or a breeder puppy, we have plenty of knowledge and support for you here on the board.
I'm just removing the Petfinder link as I don't want to risk further specific comments on the rescue involved. No implications implied but I don't want to have further public comments specific to these listings.