I don't have a lot of experience of gettin my pictures printed, but a have made a photobook and a three posters on high quality art paper. One step I see as important there is soft-proofing. As a screen can display more colors than what can be printed, some of the colors you get in your editing will be lost or blown out when transphered to a physical medium.
Because of this some printing services will offer the possibility to download ICC-profiles for the printing processes and media they print on. You can download them and install them on your PC. After editing the image you want printed you can load those profiles into your editing software of choice (I know Photoshop, Affinity Photo and Capture One Pro 20 can do this). The profiles will then simulate the look of your picture, when printed on the medium the specific ICC-profile is simulating. Some softwares will also allow to display the color gamut, the color range which the chosen printing process can realize on the chosen medium and will mark all colors that are out of the possible range. You can now further edit your picture to fit into the possible color range or choose a different paper type with a different profile and retry.
It's very hard to get all colors into the possible gamut range, but the right choice of paper (matte, glossy) and printing type can influence the out of bound range a lot, but that is different for every picture and print you make.