o/

I'm terrible too, the point of a music game for me is to relax, isn't it? That's why I mostly play some old james bond songs, deep house, chill-out, stuff like that. Juts stay away from dubstep and noisy rock songs and you'll be fine :)

Portal 1 & 2 are both awesome and can easily run in a crappy pc with no lag at all.
I don't know if you like music driven games, but I'm a big fan, so, Audiosurf, Symphony, Soundodger+ and Sequence are all 100% recommended.
To The Moon is a history driven game that will definitely touch you, Gone Home is quite good too.
Hotline Miami is pure awesomeness, has an awesome soundtrack and bring a very good arcade felling too!
Eufloria is beautiful and relaxing.
The Walking Dead and The Wolf Among Us are probably the best history driven games out there, and since there's very little gameplay it would probably run ok for you.

I can recommend you a few good games that run on crappy computers, I was stuck with one for 6 months last year when my laptop broke... lol.