You can absolutely stream through your computer. The Netflix site is fairly simple and easy to use and I've always found the streaming quality to be above average. That said, you will need a Roku-box type device in order to stream it directly to your TV. You always have the option to connect a laptop to the TV (which requires the right ports and the right connector cables) but that can be a hassle with setting it up and then wanting to use the laptop away from the TV.
You can also stream Netflix through gaming devices like the Xbox360 and PS3 if that's of interest at all.