OK, here's where I know what a beginner I really am - when I can't keep up with answers in a "photography beginners' forum"!
...
Don't feel alone; that's how we
all started out.
... I'm scanning the photo, not the negative - should I be doing that? And if I can change to higher than 300 dpi, will quality really improve?
Ah, there's the problem.
For one, even when scanning the print at 300ppi you are probably still not getting what the magazine considers a high resolution photo. If the original print is a 4x6" print, a 300ppi scan will yield a 1200x1800 pixel image. Not bad, but not really particularily high resolution. It would, in theory, be sharp enough for magazine if the reproduced image was no larger than 4x6". But theory only goes so far.
The other issue is that it is a print. A color print doesn't contain all that much detail. An excellent, very high quality print may contain detail fine enough to require a 300ppi scan, but most aren't detailed enough to require anything higher than 200ppi. If you are scanning a small 4x6" machine made print it only contains a modest portion of the detail in the original negative or slide. A 200-300ppi scan will capture all that's in the print. After all, print materials are designed for producing prints that look sharp to the naked eye and you can't see detail smaller than a 200-300ppi scan records. They aren't designed to record image detail any smaller.
A higher resolution scan will yield more pixels but not more detail. It might fool the magazine into accepting the image, but only if they don't try to print it any larger than 4x6". To get true high resolution images to magazine standards you would have to scan an 11x17 print at 300ppi (3300x5100 pixels, roughly the same number of pixels as a 3200ppi scan of a 35mm negative but not as much detail) or possibly a 300ppi scan from an 8x12 (2400x3600 pixels).
What you really need is either a good dedicated film scanner or one of the better flatbed scanners that can scan film (EPSON v700 or v750). Either will in the $500USD range and up. The only thing less expensive that would be adequate and that I have any experience with (and that second hand) is the EPSON v500.