These, of the dog and the cyclist, look pretty normal for a high-speed film to my eye. What film, speed and is there any cropping in these shots? (I consider anything 400 and up high speed).
For B&W films, the appearance of grain can be strongly influenced by the processing, and the particular developer. With color, the ability to influence grain in processing is much more limited. Aside from exposure and framing, there is pretty much nothing that can be done in the camera. The only real choice is a slower film.
Another factor is the scan resolution, some resolutions will cause artifacts that accentuate grain, the primary way to avoid that is to scan at various resolutions and see what looks best. Since you aren't doing the scanning, you may not have much choice there. Scanning discussions are pretty limited here, the sister site,
http://www.hybridphoto.com, has discussions of all things digital as it relates to film.