I use numerical value arrays to create DAT files (save). But is there some sort of way to store string values in an array? This would be helpful for the type of program I am making.

Not in DAT files, sadly. String arrays cannot be saved as DAT. However, you can save a string array to a regular file, using PRGEDIT and PRGSET. You go through each item of the string array and save it to a line, then for loading, you use PRGGET$() and load each line back into a string array.