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 [lightroom-3] tag you added to your question. It's a fair choice for this. There are two limitations in Lightroom that make it less than ideal for your application however:

1. Lightroom has no built-in way to talk to a scanner. Most image editing programs support WIA, TWAIN or both, so that you can scan something straight into the application. Not Lightroom. You'll have to scan with separate software and import that into Lightroom somehow.

   There are ways to automate this scan-and-import procedure so that it works mostly like WIA or TWAIN. For example, if you use VueScan as your scanner software, you can configure it so that its scan-to-file directory is the same as Lightroom's auto-import folder.

2. A much bigger problem is that Lightroom's ability to remove dust and speckles is limited compared to a full-blown pixel editor like Photoshop. Lightroom's quick heal tool is fine for removing small dust specks, but when you get fibers and such — very common when scanning slides, if only as sheddings from the cardboard frame — the inability to heal non-circular areas means you have to enlarge the tool to cover much more area than is strictly necessary. Sometimes you can get away with this, but other times the limitation effectively prevents you from fixing the problem within Lightroom.

   Lightroom lets you configure it to work nicely with an external photo editor, and of course it works especially nice with Photoshop or Photoshop Elements.

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:

• Corel PHOTO-PAINT: ~$320 street as part of CorelDRAW! graphics suite
• Paintshop Pro: ~$80 street
• Photoshop Elements: ~$65 street
• Gimp: free
• Paint.net: free

(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.