I'm also new in photography and had the same question as you. After days and days of reading, I decided to buy Nikon D5100. This is entry lever DSLR with good sensor and image quality, and really good price. This DSLR comes with standard kit Nikkor DX 18-55 which is good for begginers, and also for portrait shots. Yesterday I took on makro photo of flower and it looks like:
You should really read reviews of Canon and Nikon entry level DSLR-s to chose which one best fits to you. Good page to start is http://snapsort.com/compare, where you can compare cameras which you are interested in, and learn something about camera specifications.
Also, there are online guides, and books which explains how to buy new camera. These are links I followed:
and of course http://www.photo.stackexchange.com :)
Hope, I helped!