Hi there! I recommend checking out this guide (and bookmarking it too!)
Forum/viewtopic.php?f=20&t=4470908 It has information on what all the values mean that you'll see on the site, as well as how that translates into rare pets. Most very rare pets are older, from around 2009 or so, unless they're store pets which can sometimes be very rare but newer, depending on how many people buy them. With the recent internet event rares, you probably won't be able to get any very rare pets, as with the way years and rarities work, you would need hundreds of 2022 rares in order to equal 1 2009 rare.
The first few posts on the link I gave is way better at explaining this than I am though!