The number 1024 would at least take 2-4 bytes (so 16-32 bits), as you need to know where the number ends and where it starts, and so it must have a fixed size. If your positions are very big, like 124058936, you would need to use 4 bytes per numbers (which would be better than 9 bytes as a string representation).
Using binary files you'll need of a way to know where the string starts and end, too. You can do this storing a byte before it, with its length, and reading the string like this:
byte[] arr = new byte[in.readByte()]; // in.readByte()*2 if the string is encoded in 16 bits
in.read(arr); // in is a FileInputStream / RandomAccessFile
String yourString = new String(arr, "US-ASCII");
The other possiblity would be terminating your string with a null character (00), but you would need to create your own implementation for that, as no readers support it by default (AFAIK).
Now, is it really worth storing it as binary data? That really depends on how big your positions are (because the strings, if in the text version are separated from their position with a space, would take the same amount of bytes).
My recommendation is that you use the text version, as it will probably be easier to parse and more readable.
About using one or two files, it doesn't really matter. You can combine text and binary in the same file, and it would take the same space (though making it in two separated files will always take a bit more space, and it might make it more messy to edit).