Here's the way I looked at it. The more pets you have, the more achievements you will most likely get, and lots of those come with rewards that may be rare pets themselves. In my journeys collecting all of the wild pets in the game, I would always capture the first one I spotted. This is imperative on PVP servers, especially if you are fighting and trying to capture some rare pet that you have been searching ages for.
Then, after capturing the first you come across, continue looking around for maybe 5 minutes max in the area where those pets spawn and search for an uncommon or a rare. If you don't find one, move on to the next pet you need. Lots of times, you may find that uncommon or a rare as a second or third pet in a battle versus a completely different pet when you aren't even looking for it any more. Just continue doing this over and over and eventually you will have a, well, menagerie of uncommon and rares, without even much effort.
After you have captured all the wild pets in your game, make it your mission to, say, complete a zone every day by capturing all rares in a zone that you are missing, and doing so one zone per day. Setting goals for yourself will help you eventually turn all of those Uncommon and below into Rares. It's doable, trust me. Sometimes it can be very, very frustrating. I remember I spent 2 hours straight about a week ago trying to find a rare turkey in Twilight Highlands and HAD to have gone through 50+ of them when finally a rare shows up as a secondary when I battle a Highlands Skunk. I almost jumped out of my chair over a standard, non-special rare, lol, but it was the last one I needed for Twilight Highlands.
Oh, and due to the relative fact that Flawless Battle-Stones are more fairly "common" now (you know what I mean), don't be afraid to use one on that Minfernal, Shadow Sporebat, Unborn Val'kyr (which I personally think is overratted
I hope this helps, maybe even only a little bit. If not, oh well, I tried.