Another less considered part of the chain is the actual recording quality of the albums you play. Without a doubt a poor recording on a great rig will still sound poor, just less so. A good recording on even a moderate system is certainly going to bring-out the best in the system. Aside from that, I have to concur that speakers/headphones are one part of the chain that can dramatically improve the sound quality and as such the SR60i is a nice set, but it won't be up to the task of really improving your listening experience beyond a point.
If you like the Grado sound, and many do, consider the SR225, espescially if you can get a used set. The consensus seems to be that of the SR range the 225 is the best value for the money and can be far more versatile than only a rock can. I had my 225s for more than two years and loved them. I listened to jazz, some electronica such as Thievery Corporation, Chemical Brothers, Peter Gabriel, Tool, Rush, Holly Cole Trio .... and found the 225 to be very capable. I would strongly encourage you to invest in your headphones first as you are most likely to benefit from such a move far more than any other move at this juncture, IMO only of course.