If you don't have the money to buy an AVR, what's the point of getting 5.1? That converter you linked to looks like it has only one output, so all of your speakers would basically have the same sound, fully negating the point of 5.1.
I agree with the posters above; either a 2.0 or 2.1 (and if you want stereo sound, you'd still need an AVR), or probably the best option on a tight budget is a soundbar (there are a whole host of them which are very inexpensive).
The other option is to look on AVS forums for your model of TV; there might be settings for your internal TV speakers which make it sound much better. I had a Samsung LCD a few years ago with really crappy sound and found some equalizer settings over here which improved the sound dramatically to the point where I didn't need separate speakers.