You can stream from your computer and there are advantages to doing so. It is easier to search for things and add them to your queue on a computer. There are sources available on your computer that aren't on a roku.
Using a roku is a more tv/vcr-like experience. There are sources available on the roku which may not be readily apparent on your pc. Streaming netflix is smoother on my roku (1) than my four year old laptop.
Start with your computer. When you have an extra $50 or so get a roku. I still use both.