These cheaper cuts of meat at perfect for soups as a long slow wet cooking is a great way to prepare tougher cuts of meat.
I used to make soup bases all the time and then freeze them in small quantities to finish as soups/stews later.
Cut the roast into the size of piece you want for your finished soup. Remember that soups are the most attractive if the pieces of the meat and vege are relatively the same size. For a stew I typically do 1 to 1-1/2" chunks, four a different soup it would depend on what I wanted as a finished product, all the way down to possibly 1/2" chunks. If you want small pieces it can be a help to slice the roast into the 1/2" slices, lay them on a platter and put the platter in the freezer just long enough for the meat to "firm up" a bit, will make it easier to cut up.
Then I will salt and pepper the meat and brown it over medium heat, this can be done in batches if there is too much meat to brown all at once. I like to do this in the bottom of my stock pot as the sides of the pot keep it from spattering. Don't crowd the browning meat in the pan or it won't brown property. During browning the meat should be sizzling merrily BUT NOT SMOKING if it's smoking the heat is too high. It's not necessary to cook the meat all the way through, you just want to brown / caramelize the meat, it adds a lot of flavor. I typically use a mix of half butter and half olive oil for this step. Cooking the meat til it's tender doesn't require much attention but it does take time, can be as long as a couple of hours or so. I like to do this on cold days when I am going to be home anyway, I just check the meat occasionally. If I intend to serve the soup/stew that day I ALWAYS start this very early, it's fine to set it aside for a while and heat it up later but impossible to hurry the process when you have a table full of hungry people.
Once the meat is all the way browned, I add stock (you can use water but stock gives a richer soup), bring to a simmer then turn down til it's barely bubbling and cook til the meat is completely tender. At this point, you have a soup base and can refrigerate it for three days or freeze for much longer. I find freezer bags work well for this, I lay them out flat in the freezer and once frozen they can be be stacked very conveniently.
To make soup from your soup base heat up the base and add your cut up vegetables. Vegetables can be added directly raw but I get a better flavor by lightly sautéing the veges first in a little butter to brown/caramelize them just a bit and then add them to the soup base and cook them til the desired tenderness.
I will cut all my vegetable pieces to roughly the same size and add them to the pot by order of "hardness" so they all get tender at about the same time. You can use any herbs or spices you like and tomato products if that works for your soup.
I used to always keep beef and lamb soup ' stew bases in the freezer for easy weekday meals.