It's tough to advise on whether your grandson is mature enough to appreciate what the watch symbolizes, without us knowing him personally. There are lots of 24 year olds out there that can appreciate the watch and it's family lineage and would happily care for it...but there also lots of 24 years olds out there that maybe don't have enough life experience to really appreciate the memories that are linked to the watch and would/could be tempted to sell it fund the next automotive project.
The fact that he's married, helps, as most married guys are less likely to sell it to fund the next extracurricular activity. 😀
But as a car guy myself, who's spent my entire adult life tinkering with cars, I can tell you that there are alot of guys out there (mostly the younger ones) that have the same passion for modifying their cars as we have for watches and don't think twice about racking up huge credit bills to "finish the build". This would be a concern for me.
My advice: Wait a couple years. I think 30 is a good age where most guys have matured and can appreciate the history and familial significance behind it. In the meantime, I would write a nice letter talking about your memories of your father wearing the watch, and what type of emotions are evoked when you put it on. Maybe a *brief* history lesson on what it meant to wear a Speedmaster in the early 70's right after the moon landing. Store the letter away in a place where it will be easily found in the event you are unable to give him the letter yourself in 5-6 years.
I would look to have the watch serviced by an independent watch maker that will respect your wishes to leave the "character" marks on the case intact and service only the mechanical components of the watch, and maybe a quick session in the ultrasonic washer for the bracelet. I would have it serviced sooner than later. You never know what the parts availability will be 5+ years from now.
It might be kind of cool for you to wear it around him a few times and talk about it. It will mean that much more to him once the time is right for you to pass it along to him, if he has some memories of you wearing it and doing stuff with him.
Regardless of which direction you go, gift now...or gift later, I hope your grandson cherishes the watch. My dad recently gifted me my grandfather's watch (a Bulova from 1949) and it's probably one of the, if not THE, best gifts I've ever received.