I think you should consider Guitar Hero World Tour: Definitive Edition. It’s a massive community mod on the original, adding songs from almost any other guitar hero ever released. Some glitch a bit and you don’t get the full character performance, as they seem to kinda chill with generic animation while playing the track, but others is just full guitar hero show. I got a (not very cheap) aliexpress guitar a pretty much like the one your linked, and it has worked me very well for a few years.