I used to own a Mesa Walkabout and have played the Rumble 500 a few times, including as a backline with a full jazz band and choir in a theater. I've played a 210/Micro AV stack in a store and at a jam in a medium-small pub but have not played the cab with the Walkabout.
For myself, between the two amps, I'd rather have the Walkabout. Between the two options presented, Rumble 500 combo vs. WA + one 210 AV, I would still rather have the Walkabout (though I'd be looking to pick up a second cab when I could), but it's not necessarily a slam dunk and would depend on your needs and use.
The Walkabout has a more flexible EQ and gain staging, sounds better (subjective and context-dependent), and will slot more easily into a wider variety of mixes (somewhat subjective -- EQ and voicing influence this). The DI is also very nice. (Though I haven't used it, I don't doubt that the Rumble's DI is acceptable, but I know the WA DI is very good -- be advised, though, that it is "post everything," including master volume, which has advantages and drawbacks -- there is a separate DI level control, though, which can help compensate for that.)
As a learning tool, I feel that the Walkabout has more to teach a developing player about gain staging and EQ than the Rumble does. Dialing the Gain up or down doesn't just affect the S/N ratio or the level of drive, but influences the note-envelope and "touch" in an organic way. The Walkabout, like the Rumble, has some baked-in voicing -- I tend to go for more neutral/evenly-voiced stuff these days -- but, again, it's a classic sound, toneful and flexible (via Gain and EQ). If you told me that I had to lay down some tracks over the next week for a mystery project using one of the amps, I'd pick the Walkabout, no question.
For the Rumble, it's light, louder than you'd expect, straightforward to use, and can sound great in the right setting. I don't know that I'd call it boxy or dull, but it can get boomy and there is a hole somewhere in the mids/upper mids that you can't address with EQ. (I've not played a Rumble head with another cab, but my impression, in the case of the combo, is that this has more to do with the cab than with the head.)
To be fair, I was still able to dial-in a good sound for the aforementioned gig (got compliments, even) and play it successfully, but I found the process of working around the boom (some rooms/stages are just tough, but the Rumble doesn't help itself, here) and the hole in the mids annoying and I think that, with the Walkabout and a good cab, I'd have had more leeway in dialing-in workable tones.
I could see the control and EQ setup for the WA being frustrating for a beginner. Some patience and maybe a little guidance would be helpful with that. The Rumble is more straight forward (and there's nothing else to carry or set up).
Both with the 210 AVs and in general (assuming both amps are using cabs of similar efficiency), the Rumble has a volume advantage over the Walkabout -- the Rumble with two tens will be roughly as loud as a Walkabout with three, with four tens, about as loud as a WA with six.
At the aforementioned pub Blues jam (louder than it should have been but not crazy as such things go), the single 210 AV was keeping up, but just (the amp was running out of headroom, but the cab was starting to strain, too). A stack of two would have felt and sounded more full, comfortable, and articulate. I feel comfortable saying that the Rumble 210 combo would have kept up fine on its own.
On the other hand, while the 210 AVs have less native bass, I see them being better behaved (less boomy, better through the mids) on more stages.
[Note: Folks used often to run the Walkabout with three 8 Ohm cabs as a way of making it more viable in loud settings -- I contemplated doing the same for awhile -- but, though Mesa winked at it, it was never officially supported and is now actively discouraged, so I wouldn't do it if you want your Walkabout to live a long, happy life.]
If, someday, you decide two 210 AVs aren't enough, you might need to look into different cabs. With 165 Watts at 8 Ohms and 300 Watts at 4 Ohms, you might need a little more cab than you would with a 500 Watt head. I used to play mine through a fairly efficient (~100 dB/W/m) and mid-forward, 4 Ohm 2x12 and, with loud people in loud clubs, it wasn't enough. The Markbass F500 I also had at the time (compact, 500 Watt class D head -- same rating as the Rumble), with that cab provided noticeably more headroom.
Using an HPF (fDeck HPF3) in the effects loop helped but, if I were to play similar gigs with the WA today, I'd be looking for an efficient 2x15 setup or similar (and using the HPF, at least in louder settings, though that's not their only use).
All that said, two 210 AVs and a Mesa Walkabout are a way better and more capable rig than a lot of bass players start with and would be enough for everything you've described in the OP. One -- well, it's a medium-duty 210. There's a lot that you can do with it, but there are limits.
If you do push the WA's power section hard (and feel like channeling some Jack Bruce), it overdrives gloriously (watch the cab(s), though, if you do).
If you and your son can try the rigs first, I would -- for all I've said, he might like the Rumble more (and it, too, would be a big improvement over playing through his guitar amp -- careful of the speakers, doing that, btw). The Rumble does have some things (power, clean SPL potential, convenience) over the Walkabout.
I'd be curious what other cabs might be available to you, but if I had a choice between the Rumble and WA + 210 AV to use as my only rig, I'd take the latter, but to feel comfortable playing out in different settings, I'd be looking to add a second 210 before long. If I were looking to play in very loud settings, I'd probably be looking at larger and more efficient cabs.
EDIT: GK combos were mentioned -- of their recent cabs and combos, those with 12" speakers sound the most balanced to me -- their 10s (Neo 410 and MB 210 combo) strike me as boomy, their 15s as middy and dry. The 12s seem to strike a decent balance. I would take the MB212 combo over the Rumble (or the MB 210).
I should also mention that while I have my opinions on the Rumble combos, I wouldn't consider my experience with them to be exhaustive -- I've certainly played worse stuff and if they work for you, they work. Both the little 25 Watt practice combo and the Rumble 500 seem to like my P-bass with flats.
EDIT AGAIN: Depending on cab selection and prices where you are, I wonder if you'd find it worthwhile to build (or have built) a cab or two -- that would depend on your comfort with the process and the price and availability of parts, but there are many good threads on the topic and some efficient designs that would make the WA sing.
