For domestic prints, don't worry about color profiles or setting any other micro-detail. Just crop the photo to the same aspect ratio. Do not bother calculating the print size vs pixel size. Use all the resolution your photo has, and the RIP and print process will do the rest for you.
For a good quality print, use photo paper, gloss or mate, but the specific settings will depend on the printer itself and from which software you are printing too.
I work in the printing business for large format vinyl, paper and mesh prints. I rarely worry about a photo color profile. Even with a big printer and RIP software, the images are printed with great colors.
And this reminds me, set your monitor colors to neutral. Do not use "warm" or "cold" color schemes in the monitor menu. Use your operating system color calibration utility and you"re set.