Hello Richard. Good morning. :-)
I'll just do a quick stock-take of my understanding of your Mauser situation. Firstly there's an M03 Pure with a 6.5x55 barrel that's lucky enough to call your house its home. And it has a Mauser M12 buddy in 9.3x62. What a great combination to start with. :-) With one or two loads worked up for each these, everything from rabbits to buffalo is possible. Choosing scopes to cover such a variety of critters could be a challenge though, particularly if longer range shooting with the 6.5 is intended.
While your daughter could make a start with the 6.5, there's no doubt a .223 Remington would be more comfortable for her. She would most likely shoot better groups with it, or hit more water filled balloons at 50 metres (always fun for beginners!) and this would make her think, 'I can do this.' :-)
A thought is, young folk are not always going to have the same interest in going out hunting as us oldies. When I first took them out with me, my children much preferred to spend a cold but sunny winter's afternoon set up nicely on a tarp, lining up one rabbit after another, hitting more than missing and eating plenty of home made fruit cake with hot chocolate while waiting for the next rabbit to come out. The times I took them on multi-kilometre hikes, up and down undulating terrain, looking for elusive pigs, possibly in persistent rain, ... well, they didn't leap at the chance to come and do that again. It might have helped if we actually saw a pig! Late night spotlighting from a Landcruiser was more to their liking, not that they could always stay awake. This is another good reason to include a .223 in your list. It's a great choice for volume shooting at rabbits or other small to medium pests, or even small game with good shots from shooting sticks. Good quality ammo of various kinds is available and hand-loading is easy. Great results are virtually assured. You'll both enjoy it.
You're lucky to have the option of suppressors. Totally banned here in Oz, for no sensible reason I can see. It seems the police are concerned we'll all turn into criminals if they're legalised, since only criminals use 'silencers'. Go figure. Notwithstanding the good sense of your authorities, I'm not convinced that ordering the threading option (or retrofit work by a local gunsmith) is necessary with a .223 - provided you feel confident that ear protection will always be used. Apologies for bringing this up again, but the screaming sound of kettles whistling in my ears is my constant companion. It's always the loudest thing I can hear, even when I'm driving my Landcruiser or sitting in a Boeing. It was a single shot from a friend's 22-250, fired too close to my head and before I had time to put on my earmuffs, that did most of the damage. All because of a rushed shot at the only rabbit we saw all day. Which he missed. Even a hit rabbit isn't worth someone's hearing. Nor a trophy Kudu.
I've never used a suppressed rifle but I've noticed that where a shooter has the choice and takes advantage, having one fitted for a new rifle is often automatic. I do wonder what I would do. I'm a little concerned that if I was carrying a suppressed rifle I might be tempted to take the occasional snap-shot, where time to fit ear-plugs and don earmuffs wasn't available. Sure, the rifle would be quieter, but it would still be loud enough to do damage, particularly if one's ears were already complaining with tinnitus. With my rifles being fully noisy, I simply do not fire them without first putting on the PPE. Before moving off this subject, I'll mention one of the side benefits of the Mauser M03's safety system, being the cocking-decocking mechanism. This cocking lever ensures that the firearm cannot discharge unexpectedly. At the very least, it will stop hearing from being damaged.
Now that a .223 is looking like a good choice, what else? :-) You mentioned a .243 Winchester as a possible alternative and I would agree that it should be seen that way. With super-accurate flat base 68 gn target bullets it would be perfect for small pests. The recoil and muzzle blast is not that much different from a .223. Losing sight picture through a scope that's zoomed in is going to happen with both for your daughter, so not a great deal of difference there. The real question is, which animals might your daughter be hunting with a .243, in your company? If the answer includes small to medium antelope and even wild boar, then a .243 Win is a good choice. Once your daughter is used to how it shoots she can progress up to loads with 95 or 100 grain bullets, which will perform appropriately on these animals, while also being far more accurate at long range in cross winds than a .223 can ever be. I see the two of you out hunting on the veldt, her with a .243 and you with the 6.5, provided you've acquired that second stock and receiver (hint - great idea!). Or you can share the one rifle, which means she won't have to carry one for miles - also a good idea.
You're right that a .243 and 6.5x55 are close to each other. I have both and use them differently. The .243 has both 68gn target loads (used for rabbits and foxes) and 95gn hunting loads prepared and sighted in. I click the scope to switch between the two, with perfectly accurate results out to 300 metres. The 6.5 has only one load made up, being 140gn high ballistic coefficient hunting bullets (by Berger), for use on pigs at long range. It'll do 500 metres without a problem.
Another way of looking at this is, if you get a .223 and the two of you are out with this and your 6.5, well you've got a lot of flexibility there. Once your daughter is ready, she'll be able to use the 6.5 successfully and comfortably. This would be the most flexible pairing, at the lower end of the power scale.
Now let's move up the scale a bit. Given that we're talking about 'wants' more than 'needs', and that you're in South Africa with its interesting terrain, it's an opportunity to look at the gap between 6.5x55 and 9.3x62. I also note that you've mentioned .338, meaning your not shying away from magnum style power, blast and recoil. The assumption on my behalf is that Mauser must have indicated that they'll make barrels for people in pretty well any calibre they're capable of. Bewdy! Take advantage while you can.
Some shooters appear to be virtually immune to blast and recoil. I'm not. For me it largely depends on what I'm aiming at. I do not enjoy sighting in a 30-06 at a paper target, even a Mauser M03 which helps with the recoil quite well. But, if it's a pig jogging along at 60 metres distance and I'm free standing or steadying against a tree - the recoil feels like a .223. :-) Exaggerating, of course, but it's curious how real hunting changes our experience of blast and recoil.
Perhaps, instead of a 338 Win Mag, 338 Blaser Mag or 8x68S, which, as you've pointed out, are close to 9.3mm in bullet types and knockdown power, a choice that would give you more opportunities would be a 300 Win Mag. Very accurate, great for long distances, hard hitting, lots of ammo choices and manageable recoil for those who are inclined to indulge in such things. No question, a .338 has more punch than a .300, but it does also tend to belt up the shooter a fair bit, especially if shooting prone with a bipod at longer range targets. You can do this with a .300 and not feel like you need to call an ambulance.
An alternative that people keep coming back to, because it's an excellent alternative, is the 30-06. I love this calibre. It's ridiculously flexible, although most of us end up using 180 grain hunting projectiles, because it's not the only rifle we have. It does still wallop the shoulder, but only so much that you know you've fired an icon. It does the job down range in a most satisfying way, without making you regret the Magnum fever you had when ordering. It makes you feel clever. It's efficient. The cartridge design just looks ... right.
And since we're talking about 30-06, we have to take one little side-step and switch over to one of the absolute gems of shooting development and hunting history. Anyone who has followed my blog knows where I'm going. Drum roll please.
The 270 Winchester. :-D I literally smile every night before I go to sleep, thinking about how long I waited before getting a 270 and enjoying the fact that I now have one, in a Mauser M03 no less, and that it's everything the famous hunters and gun writers have always said it was. Simply perfect.
Sure, a 270 is close to your 6.5, but it actually has quite a bit more punch, without the bordeline offensiveness of the 30-06's recoil.
Decisions, decisions. Let's say you'd like to keep it down to two new barrels and that the focus is the best fit with what you already have, while considering what will work well for your daughter, along with your intended applications. In this light, I'm thinking .223 Remington and .300 Winchester Magnum. I see these two getting plenty of use, rather than always being left behind because they're not different enough. Rifles are like golf clubs - they're all different but there's only so many you can take. If the number is restricted for some reason, a spread is best, for a hunter.
If three new barrels is on the cards, I'd think about adding a 270 Win. It's just so easy and fun and flexible and useful and capable. It's giving yourself a treat.
Now, please write back and let me know by how much I've missed the mark. Fill in the gaps in my knowledge with some thoughts on what you'll be hunting and what the terrain will be like. Everything I've written could change. :-) It could be that it's too good an opportunity to pass over getting a .375H&H Magnum, because you want to cook home-made free-range Cape Buffalo burgers on your patio barbecue. I would be jealous if you went for one of those.
Regards, Rick.
p.s. Consider sending a private message to Derek Edgley who you can find in this thread. He might still have the subject M03 for sale. He had it made for use in Africa, but I don't think it made it there.