How can I improve print quality and color accuracy on an Epson Stylus Photo RX600?

Start with the printer, because blur and banding can also indicate a hardware issue.

1. In the Epson print settings, choose the highest photo quality mode available (for example, “best photo”), turn high-speed printing off, and disable extra processing such as smoothing.
2. In Photoshop, avoid conflicting color management. A simple starting point is to let the printer manage color, then in the printer driver use its color controls and select the appropriate RGB mode offered there.
3. Run printer maintenance: head cleaning and print-head alignment. Banding often points to clogged nozzles or misalignment.
4. Test with a simple known file, such as a grayscale step chart. This can reveal banding, color casts, and alignment problems more clearly than a photo.
5. To judge color accurately, your monitor and printer really need calibration/profiling. Without that, prints will not reliably match the screen.
6. If possible, print the same image through a standardized lab. If the lab print looks good, the issue is likely your printer setup or printer condition rather than the camera file.

Your equipment is capable of good results, but correct print settings, printer maintenance, and calibration matter a lot.