I have tricks for this. Order a nice 500 piece set of cash game chips with labelled denominations of $1 (white) $5 (red) $25 (green) $100 (black) --standard casino denominations and colors.
Here's an example I found Amazon. I'm not recommending this specific set, it looks totally fine to me but I haven't used myself. But this is about how many chips of which denominations you want. https://www.amazon.com/Brybelly-Count-Eclipse-Poker-Chip/dp/B003Y4GEIQ/ref=sr_1_10?crid=2MH8Z3KH62M9G&keywords=cash+poker+chips&qid=1682708748&s=toys-and-games&sprefix=cash+poker+chips%2Ctoys-and-games%2C129&sr=1-10
Then go on amazon and pick up 100 blue chips, a color that shouldn't be in use in the main set.
Something like these (again, look fine to me, but haven't used these specific chips so can't endorse personally): https://www.amazon.com/Rack-Me-Bundle-Lightweight-Accessories/dp/B0859HHPRF/ref=sr_1_5?crid=47NVW7S8IFSD&keywords=blue%2Bcasino%2Bchips&qid=1682709021&s=toys-and-games&sprefix=blue%2Bcasino%2Bchips%2Ctoys-and-games%2C123&sr=1-5&th=1
Your son can use the blue chips for 50 cent or 25 cent chips, and use the rest of the chips same as you guys for cash game. I'd recommend making his game .50/.50 to keep things simpler (even in a small stakes, I doubt the SB will complain too much about having to put in an extra quarter). It was unclear from your post if you want to use the same set for both games, or you want to a buy set for yourself and set for your son. In any case if you each want your own set, you'll just have to order two of the cash sets and some blue chips on the side for your son's game.
As for tourney the trick there is to just not start blinds at 10/20. There's no reason the blinds have to start at large numbers. Start the the blinds at 1/2 (if you and your son are sharing the set you can even use his blues to start them lower at .5/1) and scale them up appropriately from there, that way you can use the same cash set as a tourney set. You should have enough chips in the cash set that way, although that may not be the case for multi table tournament. You can just order a separate set of tournament chips, I'd say that worth it if you regularly host tournaments. If you host mainly cash with an occasional tournament, just use the cash chips for tourney.