I think the "how much experience do you need" question is really a "how long is a piece of string" type question. It depends on so many factors - including the personality of the person. A more confident, relaxed "have a go" type rider will probably manage better sooner than a nervous "someone tell me what to do" type.
There are places where you can put the horse at full livery and they will do absolutely everything - even to the point that you can say when you want to ride, and they will groom and tack up the horse for you - so in such a case the ownership is really just a matter of who pays the bills.
I think for anyone considering first ownership the crucial thing is to find the right level help from your instructor/livery yard, to find the right horse that will help you build your experience and confidence, and to make sure you can afford it all. One of the biggest mistakes is to buy your first horse and then find you can't afford any more lessons. An even bigger one is for a beginner/novice rider to buy a young or even unstarted horse without the money for lessons or training on the premis that they will "learn from eachother". (Sadly this happens all too often, and rarely ends happily.

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Unless you are already a very experienced rider who just doesn't happen to have had their name on the papers before, but has many years experience of shares, working on a yard etc. etc. you will almost certainly need some professional help and support at the beginning - so make sure you build that into the budget.
If you balance these factors well, ownership can be as soon or late as you want it to be!
