Don't crop or resample your image unless necessary for composition.
At your native camera size (5184px) a 36" print would be at 144 ppi, which is probably "good enough" for an acceptable print. For example, if you wanted to offer it for sale here (DPC Prints) you would only have to upsample a little bit to 150 ppi.
Basically you want the longer dimension to be about 5400 pixels (36" x 150 ppi). When I have an image close to a standard size I just add a border to bring it up to the standard print size.
To add to Paul's post, both your option 1 and 2 would produce exactly the same results because they start with images of the same pixel size.
Since the desired size matches the aspect ratio of your photo, there is no need to crop at all, and really there is no need to resample either; the printer can and will manage that. Your native image pixel dimensions will result in a very nice print at that size.
What they said. If you're using a quality printing service, they will take care of whatever upsampling may be required, Their people are always good at it. I give MY printer unsharpened images as well; he can better handle that after the other necessary adjustments are made.
Thank you very much for all the information.
I have taken everything on board but am still in a bit of a quandary.
GeneralE says Don't crop or resample your image unless necessary for composition.
Great, I usually don't have to crop.
kirbic says Since the desired size matches the aspect ratio of your photo, there is no need to crop at all, and really there is no need to resample either; the printer can and will manage that. Your native image pixel dimensions will result in a very nice print at that size.
Bear_Music says they will take care of whatever upsampling may be required.
Nothing. It doesn't matter. Those DPI figures are just what you tell your (home) printer to do when you are printing (at home), basically. If you are sending your work to a competent professional lab (not walmart or something) you just upload the processed original at full size and tell them what size you want the print to be. They have more tools and better experience than you do at preparing images for print. For example, they'll adjust paramters as needed to compensate for the different surfaces you can choose to print on; matte paper needs different values than luster or glossy paper, and so forth and so on. They'll let you know if there's an issue. If possible find someone in your city who does this kind of printing and establish a personal relationship with them It's worth it.