I have been in the printing industry and designing graphics, for all sorts of printing, for pretty much my entire adult life. Here's the best advice I can give you...
Creating any new Photoshop file for the purpose of printing, it is best practice to always create the file with the canvas size at the actual size it will be printed for the job it is created. Actually, I usually make my canvas size about a half an inch larger (on all sides) than the artwork itself.
To be able to achieve nice crisp sharp edges for any fonts and typing and any other elements that will be created directly in Photoshop, starting right from beginning at the new document set up, the document resolution is perhaps the most important. 300 Pixels Per Inch (PPI) will give you nice crisp un-pixelated artwork for the final output. I always create my documents at 400 PPI just in case I need to do some minor enlarging and scaling in the future. The downside of that is the higher the resolution of the document, the larger the file size.
Knowing the printing method which will be used at the final output is also very important. Knowing this information is also crucial for setting up your initial document. For example, if your design is ultimately going to be printed at the facility of an offset printer, cmyk a.k.a four color process, will generally be the printing method used. In this case you would create your new Photoshop document in CMYK color mode. If you were to create this document originally in RGB color mode, it would ultimately have to be converted to CMYK for the output separations for the printer. Any colors in your document that were created in RGB color mode at first, which fall outside the gamut of what CMYK could produce, would be color shifted when converting from RGB to CMYK. However, if your design will be printed using a method such as screenprinting for T-shirts or some other process which will use spot colors only (not combined with CMYK printing), you can create your document in RGB color mode and assign any of your spot color channels using any of the given color books such as Pantone matching system.
Generally, most of my designs use both Photoshop and Illustrator. For example, if I cannot create the entire design using only vector artwork in Illustrator, I will manipulate all the elements of the design in Photoshop that are raster based.. such as photographs and other flattened or rasterized elements and then save that document created in Photoshop as a .tiff file format (which enables saving the file with any transparent elements or layers). Then I will create a new Illustrator document with the same art board dimensions and color mode that are used in that saved Photoshop .tiff file. Next, once that new illustrator document has been created and is open, go to menu item File/Place and locate that .tiff file (making sure you select the "link" option) and place it into your Illustrator document. The awesome aspect of using the "link" option is if you need to go back to Photoshop and make any edits or color changes or whatever to that .tiff file and save those edits, those new updated changes from Photoshop Will be reflected in Illustrator as well. At this point, now you have all of your raster elements visible in your illustrator file and now you can add any vector items or typing words or what ever else to the document. This will absolutely ensure the cleanest, sharpest, crispy edges to the artwork.
The only time I do not follow this is exact step-by-step procedure I have outlined is when I produce the printing separations for the printer to use rather than allowing the printer to do the separations themselves. What I mean by that is, if I create any new spot channels in Photoshop that will be printed as separate colors, I will save the Photoshop document as a DCS 2.0 file format. Then I would follow the rest of the outlined procedure I previously described. Placing this DCS 2.0 (which is actually an .EPS file) into illustrator, will automatically load any spot channels I have created, directly into the illustrator swatches panel
Summing it all up, if you are hellbent on using only Photoshop, create the document starting out using the exact dimensions you will need for output, choose your color mode appropriately, 300 PPI image resolution, avoid adding any vector elements which could be added after-the-fact using illustrator.