depends on the finished size of your blocks too. If you are doing say, a 4" finished block, you need the 1"-ish strings or your won't get any fabric on your block
If you are doing a 10" block wider strings are more appropriate.
Also might depend if the strings are sashings, or will be borders, or are to be just part of a bigger standard stitched block.
You also need to think about if you are going to split the blocks and resew them, then you'd start with bigger blocks.
Bonnie Hunter has some nice free string blocks on her Free Patterns tab on her blog.
I've done all of the above, all turned out very striking! I do sew on paper because the widths aren't consistent so the finished size needs to be bigger and trimmed down because it's easy to go crooked just sewing them together in the standard way.
In this improv I used all the techniques
I made this while I was caring for my mother who had dementia. There is never time to think so I set my machine up by her chair and just sewed strings.