If it helps to any degree, I live in the "Saint-Lawrence lowland" area and most of the fossils I expect to collect are from Ordovician period. Most stones are being washed by the river so the surface is kind of smooth.

You could look at this and similar apps but they're more from the other side, you have a rock here's what you need to ask yourself to ID it. I don't use anything like that myself because I memorised the A2 rock identification flow chart we used to use at uni which was similar to that below only more complex. It sounds like you wouldn't benefit from something that complex as you aren't interested in the chemical range of formation for the individual types of the amphibole series minerals present etc... but the below should help you differentiate. You best bet for recognisable fossils are sandstone, limestone, mudstone, shale, and chalk.