All the above. I guess you are using a 35m film, but you mention ISO 125.
My experience with film and scanning is that it will have grain and other
artefacts if the scanner hasn't been well cleaned or the film has been
exposed to dust or not handled with the necessary care and and scratched.
As it is, it has its own charm. If you want to use film and still want the
quality output of a good digital SLR, you should consider the lower ISO film
(ISO 60) you can get and if you don't do your own developing, get a
professional photographic firm that does, even if it costs more. Also little
home scanners like the ones I got the Kaiser Bass 35mm Negative & Slide
scanner or the the all-in one Canon Pixma printer will not produce the quality
scanning than a professional photografic firm would. My scanning is passable,
but that is where it stays.
The best quality photographs I've seen recently have been done using
gelatine plates or large format cameras, but I am entering now a terraine
I have not practical experience and all I know is what I've read and seen in
books or at exhibitions. Others here are more knowlegeable than me.
If you like film photography, stay with it, I think it is more demanding than
digital, and experiment with different ISO films. The higher the iSO; the
more grain it will be in you photographs. There is nothing wrong with it and
ofcourse once you convert it to digital you can further manipulate the
picture, unless you want to be a purist.