Yes—GIMP is a solid Photoshop alternative for a hobbyist, especially if cost is the main concern. Based on the community feedback, it can handle the core tasks you listed: crop/resize, rotation, perspective correction, levels, curves, brightness/contrast, sharpening, denoising, red-eye removal, color fixes, and compositing/merging new backgrounds. One user even prefers some of GIMP’s tools, like its curves interface.

That said, GIMP isn’t necessarily the strongest option for every workflow, especially advanced color work, and some simpler programs may be easier if you only need basic edits.

Other alternatives mentioned:

• paint.net — free, Windows
• Paint Shop Pro — long-running Photoshop alternative
• Pixelmator — Mac option
• Picasa / Windows Live Photo Gallery — simpler basic editors
• Photoshop Elements — much cheaper than full Photoshop and close to it for many photography tasks

If you want a free, capable editor with lots of features, GIMP is a good candidate. If you want something easier for basic work, try a simpler editor; if you want a closer Photoshop-like photo tool at lower cost, Photoshop Elements is worth a look.