I like Michael's advice on this. I do likewise.
That much said, there are a few additional comments to address the questions you asked.
Firstly, in the case you asked about, you are downsizing, not up-sizing. If you wish to have a specific image resolution (PPI) - necessary for some things, but not others - when you are downsizing, in the Photoshop Image Size dialog box you would select "Bi-cubic Sharper" rather than "Bicubic Smoother". The former is for downsizing and the latter for up-sizing.
Like Michael, normally when I change the linear dimensions of an image I leave "Resample Image" UNCHECKED, I change the linear dimensions to what I want and let the PPI resolution take care of itself, as long as the PPI doesn't sink much below 240 when I am up-sizing. This is because it is best for image quality to avoid resampling as much as possible and 240 produces a very acceptable large format print (at least on Epson 4000/4800 printers where I know from personal experience).
Now, since you are REDUCING the linear dimensions in the example you asked about, when you leave "Resample Image" unchecked and change one of the linear dimensions (with "constrain proportions" on), the PPI will increase, which is fine. If you reach a point where PPI increases beyond 480, you may wish to resample down to this maximum value, because sending more than 480 PPI to the printer really achieves nothing - you are hyper-rich in resolution.
In the example you gave, moving from 240 to 265 by just changing the linear dimensions with "Resample Image" UNchecked is theoretically the best of all worlds because you are getting more resolution without any quality degradation from the resampling process - though I agree with Michael that Photoshop's new resampling algorythms are so good that within a reasonable range you won't really notice the difference.