The choice of scanner these days falls largely down to two types due to cost, flatbed or a dedicated film scanner. By far the most popular are flatbed because they can be used to scan other things other than just 35mm film and whilst the quality of their film scanning capabilities have increased in recent years, they can't really compare to the quality of a good dedicated film scanner. One of the best pages I've read on explaining why a flatbed scanner isn't as good as a dedicated film scanner is this one. However it's also not all about the resolution of the scanner itself as the figures quoted by manufacturers can, at best, be called theoretical and at worst, be called fictional.
One of the most popular flatbed scanners for scanning film was the Canon Canoscan 9000F. This scanner is advertised as having a resolution of 9600dpi, however when this scanner was used to scan a USAF-test chart at 9600dpi the resulting image only really had a resolution of just 1700dpi or just 17% of it's 'full resolution'. A full review of this scanner detailing these tests can be found here.
By comparison the Plustek 7600i dedicated film scanner 'only' has an advertised resolution of 7600dpi some 2000dpi less than the Canonscan 9000F, yet when this was used to scan the same test chart the resulting image achieved a resolution of 3250dpi. Whilst this is still 50% less than the advertised resolution it is a massive increase over what a flatbed scanner can achieve. Whilst the Plustek isn't the highest resolution dedicated film scanner it is perhaps the most affordable one that still produces very high resolution, professional quality scans. It is for this reason that I chose to buy this scanner in order to scan all of my dad's slides.
The Plustek 7600i comes in two varieties depending on which version of the Silverfast comes with it, either Silverfast Ai or Silverfast SE Plus. Unless you are planning on scanning a lot of film professionally, have a scanner that will automate the scanning of several slides/photos and therefore benefit from the use of Silverfast 8 Ai's Job Manager and require the use of IT8 Calibration then you only need Silverfast 8 SE Plus.
The Silverfast software is designed specifically and only for the scanning of both positive and negative film but it doesn't mean that you have to use this software. Vuescan is a lot cheaper and a very good alternative. However where Vuescan does have the edge is that you are able to select the brand, stock and ISO of the film used and this will ensure that the correct tone and grain is captured accurately by the software. This not only ensures that the photos look as good as they can but also saves you time later in Photoshop or Lightroom 'tweaking' them.
You can also do a certain amount of correction to exposure, contrast, saturation, colour balance etc at the scanning stage and also, if your scanner supports it, perform a multi exposure scan which can really help to capture detail within the shadows and is also handy for any underexposed shots.
The Plustek 7600i also can use an infrared scan to remove any dust and dirt which can be controlled via the Silverfast software. I actually find Silverfast very hit and miss in this regard and often find that it removes parts of the photos that aren't actually dirt or dust. Yes I could manually control what Silverfast does and does not 'fix' but the software isn't very fast at doing this and so I find it easier and quicker to just apply basic cleaning in Silverfast and then do a proper clean in Photoshop using the healing brush and clone tools. I actually found Vuescan to be a bit better and dirt and dust removal than Silverfast but even that was not without fault.
What resolution should you scan at? Personally I think a lot of this is down to personal taste and end use. The family photos I am scanning are not works of art and have no commercial value but they are priceless to me and irreplaceable. Therefore I scan these at either 7200dpi. These produce a TIFF file that I later re-save in Photshop as another TIFF file using the LZW lossless compression which has a file size of around 120MB and a size of 9650 x 6400 at 7200dpi. If these were printed at 300dpi they would produce a print measuring roughly 32 inches x 21.5 inches.
Some of the photos though are not as 'important' and these I scan at 3600dpi. These produce TIFF files that are around 27MB in size and measure around 4800 x 3250 at 3600dpi. If printed at 300dpi these would produce a print measuring roughly 16 inches x 10.75 inches.
With several hundred photos to scan it's going to take me a long time to complete and with file sizes like that I will definitely need to buy something like a 1TB hard drive to put them on and then another to back it up!