I would like to to clean up damage to and retouch under/overexposed scanned slide images, prepare the digital images with copyright symbols for use on web pages and add tags to allow image files to be 'searched' on a website under key words. I read a lot about Illustrator and that seems the right software to get on a budget, but Adobe keep pushing Photoshop CS6, which is too costly for me right now. Is Illustrator what I need to look at or is there other comparative non-Adobe software I can get that is just as good?
I don't know where you're getting your information about Adobe Illustrator, but you've been misled.
Photoshop costs about the same as Illustrator at the moment on Amazon.com, so I don't see how Illustrator is the "budget" choice. Maybe you're comparing with Photoshop Extended, but there are no features in Extended relative to standard Photoshop that you need for this.
Even if Illustrator were a lot cheaper than Photoshop, it would still not be something you should be considering for your task. Illustrator is powerful software, and it can certainly be made to do at least some of what you want, but only in the same sort of way that you can drive a nail with a Crescent wrench. It simply is not the right tool for this job.
Someone suggested Lightroom as a possible choice here, and it seems you're thinking that, too, from the
If you find yourself needing a pixel editor, there are many choices that will cost you less money than Photoshop. In fact, every alternative I'm aware of costs so much less than Photoshop that you can get Lightroom as well and still pay less for the combination. Examples:
(I've listed only Windows software on purpose, since you mentioned the Windows-only Paintshop Pro in another comment. Other platforms have additional alternatives.)
Photoshop is more powerful than all of these, by a considerable margin. You will find some people online who will try to tell you that Gimp is just as good as Photoshop, but these people clearly have never used both for extended periods. The others are even less powerful than Gimp. Nevertheless, you can do all of what you ask with all of them.
It's a question of what other features you need. If your question lists every feature you will want from a photo editor, you can pick any of them that you like. If you need other things, or expect to need other things, look at the feature lists and decide if you're willing to pay the asking price to get those features.
Something to consider about Photoshop is the ecosystem. You will find more books, more training, more plug-in software, etc. for it than for any of the others.
If I had to select something for you, knowing nothing else about you, I'd choose Photoshop Elements. (Optionally coupled with Lightroom.) It's about $65 online, it will do everything you ask, and it will likely do everything you need for quite some time. If the time comes that you outgrow it, you can directly transfer your skills to "real" Photoshop. The user interfaces are somewhat different, but the tool sets are the same, the keyboard shortcuts are the same, the file format is the same, etc.
Its unclear, can you rescan the photos with a tool that can eliminate dust at scan time? Both VueScan and SilverFast can use a special IR scan on most slide scanners to remove scratches directly.
I've used both Aperture 3 and Lightroom4 to fix images after they have been scanned. Both work. And they are, of course, great for post-processing photos when you don't need the full blown Photoshop.
Photoshop, of course, in the right hands, can do anything.