I have a printer that prints onto labels at supposedly up to 4800 DPI. https://www.primeralabel.com/lx900_features.html
I'm guessing this is mostly marketing.
I need to print onto 25mm by 51mm labels and I am trying to get the text to be very clear, what DPI should I design at?
If you don't mind waiting a few minutes for each copies and the first copy, you can use the highest resolution possible! Usually you do your own tests and see what's best for you, depending on the time you have and the quality you get. Most drivers let you change the output resolution so you don't need to prepare different files if you want to make some tests or if you're in a hurry. For example, you can set the output standard to be 300dpi for color images, 600 for grayscale and 1200 for monochrome (linearts). If you see you need more, double the resolution where needed and prepare your files accordingly.
The higher the dpi/ppi, the longer it will take to print a copy and you might not see any difference in the quality for some designs. The resolution is more a concern with raster images (eg. pictures) or vectors with very fine or light lines. So it's not just marketing, that high resolution your printer can output simply means you will get very fine details and smooth lines even if you use only one color. For pictures, you'll get more small details even though it might not be necessary or obvious.
As it was mentioned in the comments, if you use software such as Photoshop or Gimp, a minimum resolution could be 300ppi/dpi. It's also an industry standard. If you're working with vectors (Illustrator, Inkscape and Indesign), you don't need to worry about the resolution, your printer will use the maximum it can produce. No need to have your Photoshop images at 4800ppi.
A good thing to do: Always use vectors for your texts. If you want to do all your layouts in Photoshop, use a higher resolution (min. 600ppi) and export your PDF without flatenning your text layers. Your layout is a small size, you won't have much problem with performance at this dimension and resolution! It's not a bad thing to work at 600ppi anyway if you can; maybe one day you'll need that layout/image/montage to be printed a bit bigger and will be able to double its size simply by dropping the resolution back to 300ppi.
PS: When I do designs and layouts for commercial labels, I'm usually required to work at 600ppi minimum.
You need to work in vectors. Use a program like Inkscape or scribus to put your texts.
If you are using comercial software use Ilustrator, Corel Draw or In Design to add them.
I have the feeling you are confusing the 4800 dpi of the printer with the so many times mentioned 300 ppi, they are diferent units. Dots for the printer, Pixels for the file. Totally diferent unit.
For photos and backgrounds use 300 ppi. For texts use vectors.
