I understand the logic behind your choice to use a sound bar. Wife acceptance factor is a common theme around here. But in your price range, you'll get much better imaging and sound stage from separates. Besides that, if you get an Audyssey-capable receiver, your receiver can apply equalization and delay to your speakers to make sure the sound from each speaker hits your sweet spot at the same time, and overcomes any wonkiness presented by the characteristics of your room. Sound bars generally don't do that.
Unfortunately, it's hard to describe the colors of autumn to one who cannot see. If you could hear a proper 2.1 setup, you might change your mind about budget sound bars with integrated receivers.
Regarding your PC, you might consider upgrading your video card to
a GeForce GT610 or better. The video card I linked has an HDMI output, and will carry audio over HDMI. I forget what the lowest model GeForce is that handles audio over HDMI; but I'm sure if you found it, it'd only be 5 bucks cheaper or so.