Test with music you know well, if it sounds good to you then its perfect
A good system and hearing will enable you to hear flaws, but it also makes it possible to hear the small details on good records.. Boombox to entry-level hifi is a pretty big difference, hifi to high-end not so much unless you have "golden ears"
My mom can't hear a difference between extremely cheap boombox and hifi though, or maybe she doesn't care. Ignorance is bliss i suppose.
As a kid i always disliked my el-cheapo boombox for serious lack of "balls", when i was thirteen i built some kit speakers for 700marks(115â‚¬), used my dads old amp from the seventies(free), connected the old boombox from headphone out to tape-in, and was perfectly happy with the much improved ballsiness of the sound
Now i use those old speakers as speaker stands.
At that time i was also perfectly happy playing online FPS games with mono sound, and did pretty good. Imagine that. Most current gamers will probably ask what mono is...