When we relocated to the other side of the world a few years ago, we had a similar problem, literally thousands of colour slides accumulated over the years that we wanted to leave copies of some to family and friends we left behind. I never really found a practical solution but for what it's worth, here's our experience.
The basic problem is that scanning is an inherently slow process - it's a function of the way the hardware works, so we decided early on that actually scanning all the slides was a non starter in the time available. But I have a very portable projector (not a great throw but no matter for this exercise) which had a facility to turn it into a light box, where I could lay out a whole set of slides and view them all with a magnifying glass, as has been suggested. you can do this as quickly as you can lay the slides out which is much faster than even professional scanning equipment. We were then able to choose what to scan relatively quickly. This method doesn't work well for negative film - at best all you can discern is the general subject and have little idea of the detail.
Realistically, if you are going to attempt to scan all the slides to "preview", then do save them all to some kind of computer storage - pictures over the timeframe you suggest would be an extremely interesting and valuable resource for your descendants or local historians. The point is that scanning is slow, storage is very fast by comparison.
So what to scan them with? I have an old (by technology standards) flatbed scanner, a Canon 8400F, which has a dedicated slide/film scanner. It's actually part of the lid, you remove the white background for normal flatbed scanning and behind it is a second scanning light, specifically temperatured for film and slides; it also shines directly through the slides and film that you put in a carrier that clicks into place on the flatbed above the scanning lens. Although it works better than the more modern slimline scanners that use reflected light, it is slow - very slow! The carrier takes 4 mounted 35mm slides or a strip of 6 35mm film and it scans this in about a minute and a half - multiply by thousands and you see the problem!
Dedicated film scanners, a good selection of which are shown in Mark's links, are faster but to get one with a preview screen, I think is well out of your budget. But as I said before, storage is much faster than scanning so maybe you could use one of your PCs to preview and select/delete while the scanner is processing the next strip?
I think the general advice would be scan only once, not once for a preview (use a light box instead) and then a final full scan.
I do remember, if memory serves (not quite as long as you but getting there!) in the days of film cameras, there was a gubbins(for want of a better word!) called a slide duplicator that screwed into the filter attachment of the lens. You then basically took a new picture of the slide. Now if you could find such a device and screw it into the lens of a digital camera, that might be quicker than scanning. But where you'd find one, I've no idea!
Sorry not to be able to help more - good luck.