Short version: it's complicated, but mostly systems automatically do the right thing.
There are only really two classes of differences in "types of plain text" Line endings and encoding.
Line ending is what typically distinguishes plain text file transfer from "binary" as the line endings are converted to the format used on the platform,
typically this is (#13#10 pairs on windows, #10 on linux/and OSx and #13 on older mac releases, older operating systems had different conventions, or record based filesystems that did not use a lineend character at all.)
Modern TeX implementations will handle all combinations of #13 and #10 so even if you have a windows file on a linux machine (or vice versa it will work)
The other difference is encoding, that is what byte sequence is used to denote each letter. Here you can use most commonly used encodings, but you need to tell LaTeX which encoding you are using unless you only used ascii letters.
So if you are using UTF-8 (the best choice if you have no particular reason to choose something else) then you need
in the file.
if you are using ISO-8859-1 (latin-1) encoding used in most of Western Europe before systems started moving to Unicode, then you need
UTF-8 is preferred as it is a Unicode encoding rather than a language or region specific encoding. (Examples copied from this site will be in UTF-8 originally, although many editors will automatically convert if you cut and paste them into a file that is being saved with a different encoding.)
Long version: The Unicode spec.