Word of mouth/recommendations are a good place to start but definitely go with a BHS registered school and if possible I would visit a couple and pick the one that seems to suit you best. There's a basic checklist of things you should look out for - you're not necessarily looking for the biggest or smartest establishment (scruffy is fine!) but one that looks after its animals and clients well. Ponies should not look skinny/scrawny and should be bright, alert and at this time of year relatively shiny in their coats (a bit of mud/dirt is OK - although good luck to any pony trying to find mud in our parched fields at the moment!). Tack/equipment is likely to be a little old but should be clean-ish and intact, no broken or worn away straps. The instructors should interact well with the children, adapt their teaching to suit the child and go at their pace. The yard should have firm (but not overly restrictive) procedures in place for supervision of children, rules around wearing hats and other safety equipment, and for health and safety generally - and should be willing to explain all this to you if asked and answer any questions you have - cagey-ness or unwillingness to talk to parents is a big alarm bell for me!
I would expect your DD to start off with a private assessment session and from there they will either recommend private lessons or suggest a group she can join. I am a big fan of group lessons for this age (once they are able to ride without a helper and are secure enough in their seat that they won't fall off at walk, trot and canter). I think it's a lot more fun for them to learn as part of a group and for the same price they usually get more saddle time (typically an hour group session costs the same as half an hour private). Even better if the school mixes things up a bit and gets them doing mounted games, jumps, stable management and hacking as well as flatwork in the school. However this is more effort for the school and instructor than repeating the same 'formula' of lessons over and over, e.g. all walk around together, all trot around together, one by one canter to the back of the ride, repeat on both reins, finish = fine occasionally but if done repeatedly with little variation will bore and sour both ponies and riders, so watch out for that! You may find that at various stages your DD needs some private lessons to ensure she is progressing, get over an issue or block with a particular skill or just to get her ready to move up a ride level. The school should be happy for you to mix things up in this way.
Pony club is a great suggestion too. Pony Club is a national association for child riders and they have clubs for both riders with their own ponies (owned or borrowed) and those who ride at a riding school. Larger riding schools will often run their own branch of pony club 'in house'. You pay an annual membership fee to the pony club itself and then a fee for each event or 'rally' which is usually cheaper and/or longer than a regular lesson and may consist of some stable management talks, games, quizzes etc as well as a ridden session that will be more like a regular group lesson. A bit like brownies or scouts, they have a uniform and work towards 'badges', and if your branch is well established/active, they may do camps, competitions/gymkhanas, seasonal parties/special events, trips to horsey events like the International Horse Show or Olympia, and perhaps even take the children to inter-branch competitions as well (some of the smaller branches don't do the latter so check if your DD is desperate to compete). Like with scouts/brownies expect to be roped in as a parent helper, even if you are not horsey!
Sorry for the essay, hope this helps. Any more questions do ask!
