I'm just slowly making the move from chemical to digital photography, so my knowledge base is minimal.
But the bottom line for digital image quality is resolution. (The same for chemical photography, but folks tend to talk about optimum exposure and saturation.)
So the starting point for quality is the captured image ... i.e. the quality of the photos you take. For digital cameras, a high resolution is important. For analogue 35mm, it all comes down to your lenses and how well you exposed the film. If you obtain an optimum exposure with good saturation, the image will transfer well to other formats. In fact, the crisper and more well-exposed a 35mm negative or slide is ... will create more data to capture for the digital version.
Of course, once you digitize your photos you face the problem of digital memory. The smaller the file, the less resolution. No way around it.
I got the Nikon Coolscan IV ED Film Scan 2900 DPI USB. It's essentially the non-professional version of the Coolscan 4000 ED and has most of the same features. The pro version is capable of 4000 DPI resolution and the "pro-sumer" version is capable of 2900 DPI. Also the IV connects via USB cable and the 4000 connects via firewire -- which helps make the transfers faster for the higher resolution, but we're talking a difference of 20 seconds to a minute max. The Coolscan IV will scan a slide or negative in about 30-44 seconds. Longer if you use the some of the cool image features Nikon includes. Digitial ICE eliminates dust and blemishes. Digital ROC restores color to faded images. Both work exceedingly well.
The Coolscan IV will run you about $840. Good price, I think, considering you are essentially getting a professional or near-professional level machine. (Pro units usually go for 1200 to 300 bucks.)
Initially, the Coolscan seemed technically overwhelming, but in the end, I'd have to say it's very easy to use. Especially for the basics. I found I got the best results with the least frustration by scanning images at full resolution, saving to JPEG format and then doing any resizing through Photoshop. I do the color correction with the Coolscan, though to get the initial image as close to perfect as possible and the controls for using the Coolscan are very easy.
Once I'm done scanning an image, I can save the file to hard disk in several formats. But selecting regular JPEG, there is no noticeable decrease in quality (for monitors and general home printer use). That brings the original file size from about 32-35 MGbytes down to 2MGbytes. From there, I've been using Photoshop to easily resize the image to file sizes that can be used for web publishing or attaching here at Gunks.com. Each time you downsize and decrease the file size, you lose some quality, but as you can see, if you start off with a high quality image, the difference is not huge ... especially for web page display.
I know there are some real tech wizs around here who can better answer your question about resizing and losing quality.
But I've found that having a high quality original image does make a real difference. The photos I shot with my Weathermatic and the ones I shot with my Nikon FM are world's apart in terms of quality and it makes a difference through the entire process.