The Sony Alpha 65 has recently dropped in price and I think it's a very nice entry-level DSLR (really, SLT but you don't care about that right now). The camera has all the features and functions, and the same sensor, as Sony's high end pro camera, and it has very nice auto modes. When you're new, you want a camera with good automatic features, because you're going to be concentrating mostly on composing good shots, and you want to be able to do that quickly without worrying about whether your focus or white balance will be correct. The Sony A65 really shines in that area with its quick and accurate auto-focus and scene detection adjustments. It can be a completely manual camera as well, and I've needed that in some situations but not very often.
Here are some photos taken by a beginner with the Alpha 65: http://www.flickr.com/photos/77816686@N02/sets/72157635006651404/ (in that set, there's lots of action shots, some landscape shots, one panorama, and even some time exposures, one with lightning in it)
BTW, yes, I'm agreeing with the previous poster that you should try to increase your budget if you can.