I learned pretty early on with photography, "affordable" or "inexpensive" is an entirely relative term..so keeping that in mind.

Your best bet for quality is a standalone slide/film (anything that can do one can generally do the other) unit, but even a used low-end Nikon Coolscan 4000 is over $1K on ebay. So you're going to want a flatbed scanner that can also do films - the quality is fine for anything you're going to want to do, plus you get a lot more versatility in terms of both film size and ability to scan reflective stuff like prints and documents as well.

I have an Epson Perfection V750 that's utterly brilliant, it's quasi-professional though, so it will still set you back $800; though the price does include high-end scanning software and more importantly IT8 color-calibration targets - pieces of film or prints with measured blocks of colors that you scan to build an individualized color profile for your scanner. If you have the money I'd recommend it with no reservations, if just for the calibration gear ($400 a la carte!).

Otherwise, the Perfection V600 is a good choice. $200 with the resolution to pull good files from 35mm. It only scans 4 slides at a time though, I guess it depends on how much time vs. money you want to spend (the bigger models do 12).

ETA - there's also even less costly standalone "slide converters" that use a CCD chip, like in a digital camera, to capture the entire image in one go. This one is fairly highly reviewed; it's only 5Mpix output (as opposed to 12-24Mpix from a scanner depending on the resolution), but depending on the quality of your source films and what you want to do with the images, it may be a viable option. Never used one though, so I can't speak to the quality (but the price tag does make me a bit leery).

It's a RX620 that prints, makes copies, scans slides and negatives. I'm happy with it. I've had it for years and it's still going strong.

I don't know what the newer models cost, though.

the amount of time you want (or not) to spend on the processing, you might farm it out.
http://www.DigMyPics.com
http://www.ScanCafe.com

at a thrift store. Almost bought it but my old HP dinosaur still walks the walk.

I'm always seeing what appears to be relatively new scanners at thrift stores. There's also a scanner you can get for your iphone. Lots of affordable options out there other than buying a new scanner.

am clueless as to which one. There are too many to choose from and some are pretty bad.

You probably don't want an old one because SCSI is hard to set up.

Do you own one? The DPI is promising....

I have an old Minolta Dimage Scan Elite (F-2900) I bought off eBay that works really well. I had to add an interface card to an old machine to get it to work; there is a "SCSI to USB converter" out there that's a really elite kinda cable, and I could have bought one of those instead of the old machine, but it's actually less expensive to buy an old Mac and set it up as a scanning station than it is to buy that converter cable.

The Pacific Image scanner seems to be one of those love-it-or-hate-it things. I would get a copy of VueScan and try the scanner; if it doesn't work well enough for you, you can always return it.