It has been a few decades since I hunted with a bow, so some of this information may be out dated, but I doubt that, even with the constant advances in bows.
For you, you might get a great deal on a used bow from an elderly man who has had a stroke, or from a widow who is getting rid of her husbands hunting gear, or an estate sale. If you ever go to an estate sale, mention you are looking for a bow, because they may have one or more, but may not have put them out, just because they may think no one would want it.
Remember this one very important question, ask where in the house the bow was stored. If they answer "in the attic" pass on it, because storing a bow in a hot attic will dry it out and damage it, and you don't want to be anywhere near a bow when it explodes in failure because it was stored in a hot attic.
Don't go cheap on arrows. If you use old dried out (wood) arrows they can splinter before they even leave the bow, and you can end up with a long splinter driven into your arm by the bow.
For the 10 year old, you probably have to limit the bow to 30 pounds of pull. It would be a good idea to do some test with a range of bows at 30 pounds and then some above and some below that pull. Be sure he can hold the bow back steady, long enough to sight in a shot.
For your son, try to get arrows that are not too much heavier than that bow requires. Shooting an arrow rated for a 75 pound bow out of a 30 pound bow, is going to drastically reduce the range of the 30 pound bow, because the arrow is too heavy.