Unless you have an explicit specification to produce an image with exactly 300 dpi, I wouldn't worry too much about the actual resolution, as long as it's more than the specified 300 dpi (but not insanely more).
Likely, you don't even need to set the exact pixel resolution in the image (i.e. those dpi): it is the job of the designer who creates the final print to place and scale the image appropriately. Scaling will probably happen anyway due to the required margins and other printing requirements. Therefore, you can send the same image in both cases.
Only in some professional workflows the printers/designers will respect the dpi (and thus physical size) you set in the image, and this is always explicily stated in the requirements. In this case, I would just set the required physical size without resampling the image (there is a special checkbox for it in the Photoshop Resize window), and wouldn't mind the resulting odd dpi (say, 324) - unless, as I said, there is another explicit requirement to have a fixed dpi.
Now I will address the common resampling question, even though it has minor relevance in your particular case. But it's always good to be aware of the potential issue, and good that you take notice of it.
I got the impression that resizing an image by -15% should result in a higher output quality than resizing by 40 or 50%. Is that correct?
This depends on the resampling algorithm used. The main issue here is that when you downsample a raster image, it usually loses subjective sharpness. To combat this, several tactics have been devised.
One is to resample and then add a little sharpening (e.g. unsharp mask).
Another is to do stepwise resampling in multiple steps of 10-20%. It can be shown (subjectively and mathematically) that this will preserve more details and will produce sharper result compared to just a single normal resample step.
Yet another is to apply a special interpolation algorithm that adds sharpness while resampling.
Photoshop (as well as most specialised software) offers all of these methods. If you open the Resize window, you'll see a selector for the resamplig method. Normally, it is set to "Bicubic Automatic". This means it will use "Bicubic Sharper" when downsampling, i.e. the third method above.
Now, if you "naively" heed the common advice and downsample multiple times by 15% with default settings, you'll usually get an oversharpened image with ugly artefacts. This is because you effectively combined methods 2+3.
Method 2 works, and sometimes works better than 3, but only if you use the "normal" unbiased "Bicubic" resampling method.
Of course, there may be cases where even a heavier combination (or entirely different methiods) may be preferable, e.g. line art or particularly blurry photos. But in most practical cases, nowadays, you shouldn't worry too much when resizing, say, ±50% or even more in one step with default settings (using good software).