Go for a share or loan of the best schooolmaster you can afford. They don't come up for sale. At 4 your child's legs won't go past the saddle flap and the type of pony they can control at this stage will not be what they want by 6. And certainly not what they want by 8. Selling first ponies is really hard which is why people don't sell the good ones! And what your child will need and want from a pony will chnage almost year on year for a good long while. Borrow them at this stage so you can get ponies which actually suit for what your child needs right now. Buying something for them to "grow into" works with clothes but absolutely not with ponies.
I agree that a loan may be the best option and that the pony you need for the next year or two will probably not be the pony you need for a 6 year old but do not think selling a first pony is difficult, unless you become too attached, a good one will always find a new home either selling or loaning, it is finding a good one in the first place that is so hard.
If loaning or sharing is not an option, even for a loan the same applies, then find the safest small, well under 12 hands, pony you can, don't worry about breed or age look for a kind pony that will be happy to stand to be brushed for ages, is good on the LR but allows the child to be "in control" rather than the leader having to hang onto it and see it in the home that has outgrown it, buy/ loan with the view it is probably a stepping stone to a pony that will go off lead as many LR ponies are best doing that and are not all great for the next stage, although with care many will be fine in the right situations.
Take time to look, ask loads of questions, go for a good temperament over everything else, your child is precious you dont want to put them at risk with a project pony that may not be suitable.
I would avoid Section As and go for a Section B instead. I find Sec As are inherently cheeky and the Bs are far more placid.
I was a TINY eight year old when I got my first 12.2 Sec B and she saw me through till I was sixteen!
I would also avoid Shetlands - again, very cheeky and will be outgrown very quickly. Something older, been there, done that, is what you want, but some young ponies are old in a young body too, so don't discount them entirely.