I have a Nikon Coolscan IV, which is a 35mm dedicated negative scanner. If you have a lot, a dedicated negative scanner is going to produce much better results, and be easier to use, than a flatbed scanner with a converter. The key thing to realise is that its not an issue of pixels - its about the dmax - the dynamic range if you like. These things are expensive for a reason.
You mentioned both black and white and Kodachrome. Be aware that all scanner types can struggle with these two negative types. Black and white negatives that have been traditionally developed (i.e. not a C41 process) will not tolerate an infrared channel scan, which means you cannot remove dust and scratches automatically. If your negs are dusty, therefore, think carefully about post-processing, because regardless of what the scanner maker says, you could hit issues. As for Kodachromes, these also have challenges, because (so far as I understand it) they have quite a 3 dimensional makeup physically, which means that getting the scan in focus can be challenging (you can actually see this structure if you look carefully at the neg). And the colour balance is different too, though that's easily addressed. Nikon scanners have a Kodachrome setting which works pretty well - I've scanned thousands of Kodachromes from the 1950s and 1960s with excellent results - there is a very slight softening, but post-processing sharpening addresses this quite well, and Kodachromes survive very well compared to other negatives, so the overall outcome is excellent. (of course, one should really talk about positives, rather than negatives, in the case of Kodachrome...)
There is a Rocky Nook book on scanning slides and negatives, which is pretty good.
According to Lightroom, I have scanned about 10,000 old negatives and slides, dating back to the 1950s. So I can heartily recommend the Nikon scanners (even though I shoot on Canon kit...). They crop up second hand quite regularly. No one makes decent negative scanners new anymore...