You should definitely aim for having having at least something around the level of an HD 598, M50 et al.
The difference between these headphones and cheap ones is pretty huge. As you move up, the price will increase more than the improvement in sound quality.
Many headphones in the $100-150 bracket may sound good, while a $1000 headphone might sound great.
I partially agree with deadlylover. I could have made do with a cheaper setup, but I have grown to appreciate the features of my amplifier and I like not only how it sounds, but also how the HD 800 feels on my head compared to the HD 650. My aftermarket HD 800 cable is a bit on the heavy side though.
It all depends on the sound signature you want. I liked how it sounded when I had my HD 555 connected to an STX sound card. I just wished for more details and a better sound stage, originally. I now have this. Getting there also cost me more than 10x as much.
You ask if there is a price limit after which one may not hear a difference. Things I barely noticed before are now easy to differentiate.
It's not really a question of whether you will hear a difference, given time, but if you find the difference worth the cost.