Lightroom includes Adobe Camera Raw which can provide R, G, and B numbers for individual pixels.
I send put printing for books and large runs. If I’m only printing a dozen photos, I print them myself. If you have a lab do prints, send them what they need. They should be able to provide a profile and instructions. Quality from labs varies widely, test them.
Under $1000, Epson R3000, Epson R2880, or Epson R2000, would probably suite. Then you need to get suitable paper, which Epson also makes.