I think when you couple the fact that you're new to the world of DSLRs and you want a preferably free photo organizer I think iPhone is actually your best bet. It is not free if you don't currently have iPhoto, but it is a highly capable application for someone in your shoes. As you grow you may want to work with other applications such as Aperture or Lightroom, but right now iPhoto seems to really be powerful enough for you.
I qualify this based on the fact that there are trials for both Aperture and Lightroom and you haven't been able to identify what you want other than saying you want something more "heavyweight". What does that mean exactly? Are you looking for something that is taxing on your system, Aperture is where it is at. Are you looking for something that gives you the best RAW workflow? Both Aperture and Lightroom are highly capable and will take care of you, and then again so will iPhoto.
You see, it is my opinion that Aperture does not offer enough over iPhoto that would warrant the price tag for the casual photographer. iPhoto has been handling RAW files long enough that even the casual photographer will find iPhoto just fine. Also, it is my opinion that aside from basic RAW editing neither iPhoto or Aperture (or even lightroom for that matter) are useful enough. I believe all three applications do need to be accompanied by Photoshop Elements or Photoshop CS2/3, depending upon your needs.
Again, all three applications are supposed to be great for digital file workflow. If you're a casual shooter then iPhoto should be ok. If you're working more towards advanced amateur or professional then Aperture or Lightroom may suit your needs better.
Give iPhoto another try, a serious try. Just because it is a "bundled" app with every new Apple computer doesn't mean it's not capable. Sure, Apple f'ed up MobileMe, but they've done rather well with iLife.
And if it matters, I was a lightroom user through their beta stages, then went to Aperture.