As others have indicated, you should scan at your scanners maximal optical resolution. That will determine the number of pixels you get. A typical 4 x 5 frame is about 96 x 120 mm, which at 1200 spi (samples per inch) will yield an image of size roughly 4500 x 5600 mm. (You will probably get a bit less because of cropping.) If you print that at 8.25 x 10.3 inches, you will be sending the printer roughly 545 ppi, which is higher than the requested 300 ppi. (Divide the number of pixels along a dimension by the linear dimension. If the aspect ratio is maintained, either dimension can be used.) That will avoid any hint of pixelization in the print, which may be what the client has in mind.
Unfortunately, although your scanner is collecting a large number of samples, it probably is not doing very well at preserving fine detail. Scanning at 1200 spi, which is equivalent to roughly 47 samples per mm can in principle deliver a resolution of half that or about 23 lp/mm. To get an 8 1/2 x 11 print out of that you need to enlarge a bit over two times which would reduce the resolution to about 10 lp/mm in the print. That would be more than enough provided your scanner actually provided that resolution in lp/mm, but you would be lucky if it actually delivered half of that. So the best you should expect in the print might be about 5 lp/mm, which may be just barely acceptable.
Your client may or may not be happy with what he gets, depending on just what he looks at. I suspect issues like composition and how you use DOF will make more difference with respect to his impression of sharpness than the above analysis would suggest. Also applying a moderate degree of sharpening in your photoeditor may help, but don't overdo it.
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