No, there isn't such thing as "Cartridge of the Week Club" but there almost should be.
When I bought my light-sixer a couple months ago, I decided that I would just collect the cartridges that I really wanted: Pac-Man, Breakout, Missile Command, Berzerk, Asteroids, and Adventure. That was it.
But then, eBay lots came into play. I bought my first lot just because it was cheaper to get Adventure with a few throw-ins than it was to buy Adventure by itself. But now that I have a few other games that I didn't want, I may as well just get a few more that I liked when I was a kid that are part of another eBay lot.
So, again, I went into my new hobby of collecting VCS games just wanting a few and ended up with 67... several of which are duplicates. Now, I love Pac-man enough to have him and friends tattooed on my arm, but I now have three working Pac-man carts.
I also don't have much space to store anymore.
That hasn't stopped me from venturing on eBay, filtering for games under $9.99 with free shipping and finding a few games that are on my expanded "must-have" list. They have literally been showing up every week now, much like a "Cartridge of the Week Club."