If you would like to print it, don't give the print house JPEG files. Use TIFF. Meaning after Step 3.
3.1) Flatten the image
3.2) Check that at 12"x12" print size, your image is 300dpi, output image size should be 3600x3600 pixels. Resample if necessary.
3.3) Look at 100% at your picture. Check that the image is the sharpness you desire, if not, use unsharp mask to sharpen your image.
3.4) Optional: Convert from AdobeRGB to sRBG should your capture/source colourspace is AdobeRGB.
3.5) Save as TIFF uncompressed or compressed using (lossless) LZW algorithm
3.6) Send for printing.
Step 3.2 is dependent on your print house requirement. I am fully aware this may very well be a redundant step should the final output device is not really requiring 300dpi. Issue here if the following
a) In the process of from digital to printing, resampling can occur in the prime software such as PS, or in the printer driver, or in the printer device itself. If the printing device native resolution is 300dpi, it will resample the input to its requirement in the driver or the hardware. So instead of the hardware or driver doing for you, you can first do it in the prime S/W first.
b) Staffs in print house are very static at times. Should you give them a 240dpi image, they will just stretch it for you in the canvas if they are using PageMaker or InDesign. I do remember some don't use PS for printing, because they want to control the output on the actual paper. PageMaker or InDesign gives better control. They will also soft profile it to CMYK for preview. You will want to take a look in the process. Ask them to soft profile it to their printer to show you what is the actual colour output when printed. It doesn't have to look the same as you see it in your display. It is common that printed output looks abit pale and less vibrant. You can request them to do some minor adjustment for you to make it looks the way you wanted.
Do you finally get what is required of you to print ?